# Measurement: Making Conversions

I’ll admit, making conversions with measurement has always been difficult for me. Probably because I don’t apply this type of math on a daily basis (as you can most likely say for most people unless they do it regularly for their jobs). Add the fact that we teach the metric system, but don’t really use it. In researching a good way to teach measurement conversions, especially for 5th grade and up, I came upon a strategy which I will share below. If you try it, let me know how it works in your class.  I’m also going to share the visual for standard liquid measures as I believe it really helps think about how many cups in a quart, pints in a gallon, etc.

Here’s the liquid measure guide

G=gallon, Q= quart, P=pint, C=cup. An interesting tidbit regarding the words:  cup is the smallest unit and it has just 3 letters. Pint is next in size with 4 letters. Quart has 5 letters. Gallon has 6 letters.  So just thinking about the size of the word might be enough for some students to relate to these units.

Steps for students to make this:

1. Have 4 different markers ready, one for each unit.  I recommend students draw with pencil first, then trace with marker because they most likely will have to try more than once to make the shape a good size.
2. Make a giant capital G in one color. Try to make it take up almost the whole page with a vertical orientation. I tell them to square it off (like shown in the picture).
3. Then draw 4 Q’s inside as shown (different color). I kind of square them off as well to make room for the other parts. 4 quarts = 1 gallon.
4. Draw 2 P’s inside each Q (a third color). 2 pints = 1 quart
5. Draw 2 C’s inside each P (a fourth color).  2 cups = 1 pint
6. Now practice making equalities with various questions: How many cups in a quart? How many cups in a gallon? How many pints in 2 quarts, etc.

Other measurement conversions (metric, standard, length, liquid, etc.)

This method was described on the NCTM forum by a high school teacher, which I saved a few years ago. I hadn’t thought about it until recently when I needed to work with a 5th grader. I know there are rules out there like this:  Going from a smaller unit to a larger unit = divide; Going from a larger unit to a smaller unit = multiply.  But it’s always helpful to have 2 strategies. If you can’t remember whether to multiply or divide, then this strategy will help do it for you.

I think the illustrations speak for themselves, but the keys are as follows:

1. In step 1, rewrite the problem in fraction form. Place the labels of the units diagonally across from each other. This is so they will “cancel out”. Place an “x” sign. As you will notice in step 3, the way the fraction is written will determine whether you multiply or divide (which relates to the above . . . smaller to larger unit = divide.; larger to smaller unit = multiply).
2. In step 2, determine how many ___ in 1 _____. If needed, there are many charts available on TPT or Pinterest to help reference the correct conversion regarding customary or metric systems.
3. In step 3, complete the equation.

Have a terrific week! Happy measuring!

# Math Virtual Manipulatives

Today’s post is a recommdendation of several math websites with FREE virtual manipulatives.  Each site has their advantages and disadvantages, and you really just need to play around with them to decide which ones have the features and manipulatives you like best.

• Use of these help children of all grade levels with this math progression (from concrete to pictorial, to abstract).
• They are FREE, so no need to order and pay for them via a math catalog.
• If you load them onto your students’ ipads or chromebooks, there is no need to get out the tubs of manipulatives in the class (which we all know get dirty, and it takes half of the class period to distribute them IF there are even enough).
• Students can have their own set right in front of them.
• You can give the links to parents for students to use at home.
• While these are virtual on the screen, students can still manipulate them which is almost as good as the concrete objects.
• The teacher can save time without having to draw geometric shapes, rulers, base ten, etc. on the board.
• They are great for problem solving projects:
• How many different ways can you use the square tiles to show an area of 24 in the shape of a rectangle?
• How many different ways can you show 1/2 with the fraction bars or circles?
• Create shapes with angles that measure _____, _____, and _____ degrees.
• With the balance scale, show 3 x 6 on one side and balance it with another multiplication expression.
• How many different geometric shapes can you make using same size triangles? (example: 2 triangles can make a square)
• What are some you’d like to share with others in this blog???

Didax virtual manipulatives

Math Learning Center apps

This is a new one I just found out about via an online math conference. It has some really cool features. The activities and lessons are more for upper elementary, but the manipulatives are for any age group.

# Phonics Part 8: More Vowels and Consonants

Do your students (K-5) really know the difference between vowels and consonants? Do they think you are talking about the continents instead?? Can they name the 5 vowels and both vowel sounds with ease? The more I work with individual students, the more I realize they often DON’T know or have a hard time articulating what they are.  So if they are confused, then are they really paying attention when we rattle along using terms such as cvc, cvce, vowel teams, vowel pairs, consonant blends, etc.

Manipulate middle letter(s).

So much of our phonics instruction relies on students knowing what they are, it may be worth it to check with yours to see.  I will admit that I have assumed they have this knowledge, especially at the 3rd grade levels and above, but this is not always the case.

Vowels:  a, e, i, o, u

Consonants:  all of the other letters of the alphabet

Vowel sounds

• The long sound is just like saying the letter names.
• For the short vowel sounds, I recommend providing a key word or two for students to refer to such as:  short a = apple, at; short e = egg, the middle sound in red; short i = is, it; short o = on, off; short u = up, umbrella

CVC:  Consonant-vowel-consonant words

• These are words like cat, red, will, hot, bus
• They are considered “closed” syllables.
• The middle vowel usually makes the short vowel sound.
• This is helpful to apply to multi-syllabic words with closed syllables:  cac-tus, rab-bit, pic-nic, etc.

CVCE: Consonant-vowel-consonant + silent e

• These are words like cake, fine, note, mule
• The silent e gives the middle vowel the signal to make the long sound (generally).
• When there are 2 vowels within a single syllable, the vowel sound is usually the long sound.

Long vowel teams: Generally this means 2 vowels together making just one sound

• Examples:  ai, ee, ea, ie, oa, ue  (rain, sleep, team, pie, coat, glue)
• The first vowel makes the long sound, while the second vowel is silent

The above are the basics and need to be understood and mastered to better tackle digraphs, blends, and multi-syllabic words. Read other vowel and consonant information with this link to one of my previous posts: Phonics Part 3: Vowels and Consonants.

Activities to practice:

• Path games
• Matching activities
• Spelling word lists
• Word hunts for these in texts they are reading
• Word family lists

Have a wonderful week everyone!

# Parent Involvement

Today’s post will focus on some ways to start or increase parent involvement in your elementary classroom. Most of them center around ways to increase 2-way communication with them, while others are focused on how to utilize parents as volunteers within your class on a regular or by-event basis. When I was pursuing National Board Certification, I recognized parent involvement was an issue I could definitely work harder to improve, so I purposefully implemented these strategies.

Parent Communication:

1. Keep a separate log to keep track of phone, text, email, and in-person contacts (date, student name, parent name, reason, result). We all think we will remember when we last spoke to a parent about an educational issue, but why not make it easier to jog your memory? Did a parent ask you to resend a list of sight words while visiting during after-school crosswalk duty? Put it in your log and check it off when it gets done.
2. Make it a goal to contact a specific number of parents each week with good news. Have some post cards pre-made to hand out regularly.
3. Try a weekly or monthly class newsletter. This is a great communication tool to let parents know what standards you are working on, what they can do to help at home, activity ideas, sharing successes, advise them of things coming up, etc. Most of you might have school accounts for that (dojo, etc.), but often a printed form is helpful and more noticeable for parents to post on the refrigerator.
4. Start your own blog for your class. Then you can include the above newsletter type items, plus pictures, videos, links, and more. Parents love seeing their students in action . . . and feel more connected to the class and school. Add a feature for parents to respond back, such as “How can you help your child with measuring at home?” or “What is your child’s favorite _____?”

Miscellaneous parent involvement tips:

1. Invite parents to write to you about their child.  At the beginning of the year, I asked parents to write a note telling me about their child. I invited them to tell me the special things they wanted me as the teacher to know – to include their successes and proud moments. Perhaps even share the goals they have for their child, information about siblings, their feelings about homework, etc. This information was helpful to me to get to know the child better. Parents really appreciated the chance to tell about their child, and it set the stage for open communications with the parents. I hope you will try it.
2. Take pictures of students involved in classroom routines. Share these at Open House or other such events. Seeing DEAR time, small groups, math centers, partner work, math daily routines, number talks, science explorations, recess, music, library, computer lab, PE, and assemblies gives them a better picture of what their child is involved in day-to-day.
3. Continue taking pictures throughout the year. Use them for a type of scrapbook.  With the students’ help, we put together a memory book of the year’s events at school, which I did for several years. I took lots of pictures (even of routine things like eating lunch, lining up, library time, where we put our coats, etc.). Every couple of months I printed the pictures and students chose 1 or 2 to write about. After editing the writing, the pictures and written captions were put together in a memory book (big scrapbook). We added borders, stickers, and other scrapbooking type visuals. We tried to finish the main parts of it by February so it was ready to share with the parents. It was available for viewing at conference times, and students could check it out to take home for parents to see.  It was especially valuable to those parents who were not able to visit school.  I put a few comment pages in the back for parents to leave notes. You wouldn’t believe how many had a much better understanding of the complex day-to-day school events and appreciated the chance to see what really goes on at school all day. After 2-3 years of making a book version, I changed it to a digital format (power point). This way parents could each get a copy. With a digital version, you have the capability of importing graphics, etc. to make it “fancy.” I still have my books and will always cherish them.

Parents as Volunteers:

Perhaps you have some parents who you believe would be assets to your class. You may want to invite them to help you with various “chores” so you have more time to go about the business of teaching. Some of the items in the list below address parents who want to help, but can’t come in person as well as those you feel comfortable with actually being in the class at school.

Check with your school policies first. There may be specific “rules” and application procedures. FERPA is of utmost concern regarding parents and your students.

Non-classroom volunteers might help to:

1. Cut out materials
2. Assemble packets
3. Prepare for class projects, put activities/centers together
4. Laminate

In-person volunteers:

1. Duplicate materials
2. Tear out math or reading workbook pages
3. Organize book shelves
4. Laminate and assemble class activity materials
5. Assist with art or science projects
6. Put up bulletin boards
7. Help with class parties
8. Sanitize computer screens, mice, headphones

In-class tutorial help with individuals or pairs of students:

If you are lucky enough to have a parent who would be helpful with your students, I would recommend providing them with a dedicated space to pull 1-2 students. Give them a seating chart, list of students’ names and what to help with, materials to use (sight word lists, facts cards, etc.).  You may even need to meet with parents prior to tutoring to “train” them in how you would like the help.  Just like with students, you model the procedures and expectations first so there is no doubt what their role and strategies are. The key is being organized so when a parent shows up, they know immediately what to work on and won’t have to interrupt you.

1. Math facts
2. Sight words
3. Spelling words
4. Listening to reading of text
5. Vocabulary help

With the above, consider how to address the following (cell phone use in the classroom, bringing a child with them, their schedule / how long to stay, dress code . . .).  Believe me, I’ve had to deal with all of these, and I learned it’s better to tackle before hand at a “volunteer orientation” than after the fact.

Readers . . . what are some other parent involvement tips you’d like to pass along? You are invited to share your comments.

Welcome to my new subscribers . . . . and have a GREAT week!

# Welcome Back!!!

Some other tips to get prepared for your literacy lessons:

• Organize your classroom books. Small tubs that can be brought to desk pods is helpful. Labels such as these help get the books returned to the right tub:  animals, friends, plants, weather, Clifford, by author, etc.  Think about a gradual release of your reading materials so students aren’t overwhelmed at the beginning of the year.  This way you can go over procedures for book selection, silent reading, how to treat books, etc. When I was in the classroom, I selected 5 tubs to put out onto desk pods each week (1 tub per pod). These were rotated daily.  The tubs were selected based on developmental level and theme. At the beginning of the year the tubs might be: friends, school, alphabet, problem solving, etc. Students could select from the tub at their pod during the day instead of everyone gathering at the bookshelf. Each student made a bookmark with their name on it (which I laminated).  They could put their book mark in it to signal to others in their group that they wanted to continue with that book later in the day. Each group had a “captain” for the week and they were in charge of making sure the books were in good order.
• Plan for your word wall. I recommend building the word wall as the year goes along, with the children involved in placing words there (rather than coming in with a complete “busy” word wall).
• Make a pledge to keep your guided reading table cleared and ready. Do you have these materials handy? Small whiteboards, markers, erasers, pencils, letter tiles or magnetic letters, sight word cards, pointers, small magnifying glasses, post-it notes, laminated graphic organizers, small teaching reference charts . . .
• Literacy activities for students to do while you are assessing.  Get out those task cards for students to review skills from last year so you can do your required assessments. Try to include a running record if possible to help determine each child’s strategies. Procedures for the activities will be important to establish so that by your sixth week of school you will be ready to start guided reading.

General welcome back tips:

1. Sharpened pencil(s): This is my most recommended tip. Give each student 1-2 already sharpened pencils to start their first day.  I learned this the hard way. First graders couldn’t sharpen their own pencils so I just about tore my arm/shoulder up sharpening pencils for them. Plus the electric one can’t take so many attempts. So it’s worth it!!
2. Welcome bag: Check out this link for a cute poem and ideas for goody bags to welcome your students to your class: https://blog.reallygoodstuff.com/welcome-back-to-school-goodie-bags-by-hadar-maor/
3. Think about how you are going to keep contact with parents.  I recommend some of the following:
• Keep a separate log to keep track of phone, text, or email contacts (date, student name, parent name, reason, result)
• Make it a goal to contact a specific number of parents each week with good news.
• Try a weekly or monthly class newsletter. This is a great communication tool to let parents know what stds. you are working on, what they can do to help at home, activity ideas, sharing successes, advise them of things coming up, etc.
• Start your own blog for your class. Then you can include the above newsletter type items, plus pictures, etc.
4. Work to create a classroom community. I love the Responsive Classroom approach (Morning Meeting is one highly recommended routine). Everything you can do to build the sense of a classroom community will pay off in many ways!! Here is their website link to great articles and advice: https://www.responsiveclassroom.org/articles/

# Place Value Part 4 — Multiplication

In this post, I will focus on some strategies for multiplying double digit numbers (whole and decimal):  using manipulatives, the area model, partial products, and the bowtie method.  I highly recommend helping students learn these methods BEFORE the standard algorithm because it is highly linked to number sense and place value. With these methods, students should see the magnitude of the number and increase their understanding of estimation as well as the ability to determine the reasonableness of their answer. Then, when they are very versed with these methods, learn the standard algorithm and compare side by side to see how they all have the same information, but in different format. Students then have a choice of how to solve (or to use two strategies to check their answers). Try my “Choose 3 Ways” work mat as bell work or ticket in the door. Get it free here.

Using Manipulatives:  Using base ten pieces is helpful to see that multiplication means equal groups. Students build understanding at the concrete and pictorial levels first. The following free virutal manipulatives are from didax. The good thing about these is you don’t have to worry about having enough pieces for everyone!!:  https://www.didax.com/math/virtual-manipulatives.html

Area Model: This method can be illustrated with base ten manipulatives for a concrete experience. Using a frame for a multiplication table, show the two factors on each corner (see examples below for 60 x 5 and 12 x 13). Then fill in the inside of the frame with base ten pieces that match the size of the factors. You must end up making a complete square or rectangle. This makes it relatively easy to see and count the parts: 60 x 3 and 5 x 3 for the first problem and (10 x 10) + (3 x 10) + (2 x 10) + (2 x 3) for the second. I’ve included a larger problem (65 x 34) in case you are curious what that looks like. The first 2 could be managed by students with materials you have in class, but I doubt you want to tackle the last one with individual students – nor do you probably have that many base ten pieces. A drawing or model would be preferred in that case. The point of the visual example is then to connect to the boxed method of the area model, which I have shown in blank form in the examples . . . and with pictures below. I also included a photo from another good strategy I saw on google images (sorry, I don’t know the author) which also shows 12 x 13 using graph paper. Continue reading

# Place Value: Part 3 — With Number Operations +/-

Place value understanding is critical when solving addition, subtraction, multiplication, and division problems. Add fractions and decimals to the mix too! This post will focus on building on parts 1 and 2 (counting and composing and decomposing numbers by place value) to add and subtract whole numbers and decimals.

Virtual Manipulatives for Place Value:

Here is one of my favorite free websites for all kinds of virtual manipulatives. You will defintely like the base ten and place value disks. Both of these include options for decimals. The 0-120 grid is also great! You can add different colors to the numbers using the paint can.:  https://www.didax.com/math/virtual-manipulatives.html

With the above manipulatives, students can practice these basics concretely and pictorially; then transition to solving them mentally:

• 10 + single digit such as  10+7 = 17, 10 +3 = 13
• Multiple of 10 + single digit such as 20 + 4 = 24, 40 + 8 = 48
• Multiple of 100 + single or double digit such as 100 + 5 = 105, 200 + 30 = 230, 500 + 25 = 525
• 1 more, 10 more 100 more as well as 1 less, 10 less, 100 less
• Add to numbers with 9’s such as 90 + 10, 290 + 10, 1900 + 100

1. Decompose and then add or subtract
• Break numbers apart by place value and follow operation (horizontal application)
• Show regrouping with subtraction
• Applies to decimals too

2. Partial sums
• Solve in parts without “carrying” the digits. This gives students a chance to develop the full understanding of the value of the digits (vertical application)
3. Rounding
• Instead of rules about digits bigger than 5 or less than 5, rounding using a number line helps a student think about place value and where the target number falls between two benchmark numbers. Ex.:  175 comes between 100 and 200, or 175 comes between 170 and 180.

Next post will be ways to emphasize place value when solving multiplication and division problems. If you have some ideas to share, please feel free to comment.

I appreciate all of my faithful followers the past 5 years!  Thank you for viewing and passing this along to other teachers or parents. I hope you all have a restful holiday break!!

# Place Value: Part 2 — Base Ten System

Students know how to count orally, can subitize, can count on one more, know ordinal positions, and have cardinality (know that the last number counted is the number of objects). These are usually prerequisites with number sense before introducing the symbolic representation and base ten understanding.  Our system is based on the repeated groupings of ten. This is a follow up from my last post (Place Value Part 1 — counting).

There are two levels of understanding place value symbols.

• Place value:  In the number 23, the 2 has a place value representing the tens place.
• Face value:  With 23, the 2’s value is 2 tens or 20.

This shows 23 and 32 are not the same amount even though they use the same digits. Conversely, this same understanding applies to decimals. For example, .4 is the same value as .40.

Here are some ways to help students develop place value competence. Below this section are activities to help teach and practice:

1. Organize objects into groups when counting.
• If given a group of 72 objects, do students try to count them one at a time (and probably losing count somewhere along the way)?  Or, can they make specific size groups such as 10’s to see they have 7 groups of 10 and 2 extra?
• If given a group larger than 100 (like 134), do they note that 13 groups of ten is the same as 130?
2. Partition numbers into groups based on powers of ten (ones, tens, hundreds).
• Students learn that 52 = 5 tens, 2 ones = 50 + 2
• Students learn that 348 = 3 hundreds, 4 tens, 8 ones = 300 + 40 + 8
• Students learn that .45 = 4 tenths, 5 hundredths = .4 + .05
3. Realize the relationship among the different places. Using the number 67 . . .
• Most frequently it is represented as 6 tens, 7 ones.
• But it can also be represented as 5 tens, 17 ones (which by the way is crucial to understanding the regrouping process for subtraction.  Show your students a problem in which regrouping is needed for 67, with the result of 5 tens 17 ones. Ask them if 5 tens, 17 ones = 67?  How many think no?).
• 67 can also be represented as 4 tens 27 ones, and so on.

A clear understanding of these three guiding concepts of place value are very important and you will do well to thoroughly help students experience them before embarking on number operations.

Some activities to help with the above:

Organizing:

• Provide objects for students to count:  beans, cubes, tiles, candy, popcorn kernels, etc. Depending on the size of the objects, give directions such as “take a handful” or a spoonful, or a cupful. Make it a competition with a partner, who has more? who has less?  Provide different containers for students to compare which holds more or less (and thus, working a little on measurement standards and conservation of space understanding).
• Use base ten ones units.  Give an amount and after making piles of tens, have student trade each pile for a tens rod.  How many tens? How many ones?

Partitioning:

• Build given numbers with base ten pieces. Example:  “Build 47”
• Match pictures with expanded form using task cards.
• I recommend using place value pieces for KG and 1st graders because the pieces show the relationship (a tens rod is 10 ones units stuck together, the 100’s flat shows ten 10s and 100 units). For 2nd and up, it might be more feasible to use the place value disks because these allow students to work with larger amounts. I know I never had enough hundreds’ flats to build larger numbers. Here’s a link to place value disks on Amazon: Place value disks
• Use place value number strips that layer:  2000 + 500 + 30 + 8 when laid on top of each other shows the number 2,538. See sample here at Amazon: Place value layered strips
• Work on mental math thinking of adding tens and ones:  10 + 2 = 12, 30 + 5 = 35, 70 + 6 = 76. I often use this technique to show visually what we want our brain to do. These are tens and ones layered strips I made, available here for free: Digit cards 0-10 and 10-100

Relationships:

• Practice making exchanges with place value pieces. Build a number the standard way (67 = 6 tens, 7 ones). Then exchange a ten for ten ones. Verify that 5 tens 17 ones = 67.
• How many ways can you show this number? (Give a number and provide manipulative for students to check and list.)
• Using base ten rods and flats, verify that 15 tens = 1 flat + 5 tens (100 + 50)
• Show how number changes by changing the ones or the tens.

Use a 100 chart. Select a number and find what ten more or ten less would be — also 1 more, 1 less. Use the chart to show ways to count by tens other than the traditional 10, 20, 30, etc.  Try 27, 37, 47, 57. Practice counting forward as well as backwards.

Important tip when using base ten manipulatives (from personal experience):

When students are using base ten pieces, don’t allow random placement of the ones on their work mat. Why? This often means a student may not have the correct amount because they miscounted their “mess.” It also means the teacher has to spend more time when circulating the room to count their “mess” to check for correctness.

The ones cubes are organized!

All it takes is noticing the student(s) who likes to organize their ones pieces.  Their 5 pieces look like the dots on a dice or how it might look on a ten frame, or the 9 ones are in 3 rows of 3. As the teacher, you can show others how this is so helpful to you (and them) to arrange them in some kind of order. Knowing they get some choice in the order is key. And noticing how different students show the same amount in different ways is an ego booster to most students.  Finally, it really does help boost students’ understanding of number bonds when they show 5 can be 4 and 1, or 2 and 3, or 2 and 2 and 1. That’s a two for one, right?

Enjoy your place value lessons — and share some you think would also be helpful!

Take care, stay safe!

# Place Value: Part 1 (counting)

Place value is such an important math concept from KG and up. It starts with counting and recognizing amounts and in later grades plays a huge part in composing and decomposing numbers, multiplication, division, decimals, and yes . . . even fractions.  Students need a solid understanding of it to estimate and compare numbers as well. Stay tuned for ideas and freebies below.

If you look up the definition of place value in a dictionary or math glossary it’s likely to refer to “the value of the place, or position, of a digit in a number.”  But I think young students start off with a different understanding of numbers and may become confused. Does a child age 2 see their age and a quantity of 2 cookies in the same way?What about these numbers? – – Should I interpret these in terms of ones, tens, hundreds, tenths, hundredths, etc.? Does place value apply to these?

• telephone number: 123-456-7890
• address numbers: 1234 Happy Lane
• zip codes
• # on a sports jersey
• identification numbers (on badges, Social Security, etc.)
• # on a license plate

The examples above are actually referred to as nominal or nonnumeric because they are used for identification purposes and rarely have any meaning associated with place value.  For example, the address above (1234) is most likely NOT the one thousandth plus house on Happy Lane.

So on the way to understanding place value, let’s look at ways numbers are classified and the basic heirarchy even before we expect them to use the written notation for numbers:

1. Rote counting:  saying numbers in sequence
2. Counting objects:  using a 1 to 1 correspondence between number and quantity. You may have to teach how to keep track of counting objects like sliding them to the side when counting, or marking pictures with checks or circles as they are counted on paper.
3. Subitizing:  recognizing a quantity without counting (accomplished using ten frames, dot cards, dice dots, a Rekenrek, tally marks).  See my other blog posts on subitizing for more info and resources.
4. Cardinality:  associating the last number named when counting as the quantity of the set. After a child counts a set of objects, ask him/her this: “How many ___ are there?” Can they name the amount without recounting?
5. Naming the next number in the sequence:  Give a child a set to count. After announcing the amount, add one more object to see if they can name it — or do they start over and recount?  Cardinality and naming the next number are needed in order to practice the skill of counting on.
6. Concept of zero:  To a young child this means “nothing.” With place value it can be a place holder within a larger number.
7. Ordinal positions:  learning terms such as first, second, third . . . which don’t even sound like the numbers one, two, three, . . .
8. Part-Whole relationship:  recognizing that quantities can be decomposed different ways. With 5 objects, can student show different combinations such as two and three, four and one, five and zero.  I often refer to this as number bonds.

The message with today’s blog is to make sure young children have a firm understanding of the above before use of number symbols and teaching about “tens and ones.” I relate this to reading:  Students need to develop phonological awareness about the sounds of letters and words before associating with the printed form (which is the study of phonics).

How do you accomplish the above?

• Lots of exposure to classroom manipulatives
• Oral counting practice (even in poems and songs)
• Match objects one to one. Place objects on top of dots on dot cards and count as you go, or Match # of objects from one picture card to objects of another picture card.
• Make designs. Example:  “Using your color tiles, what design can you make with ten pieces?”
• Use ten frames and dot cards during Number Talk sessions (flash quickly and discuss how the quantity is seen).  Example — If you show a dot card with 4 which forms a square shape, do you get a variety of responses such as, “I saw two and two.” or “If it makes a square, there are 4.” See some of my Number Talk blog posts for resources.
• Use class scenarios to help children name the next number.  “There are 3 of you sitting on the carpet with me. If Megan comes to join us, how many would there be then?”
• Practice counting on with ten frames and Rekenreks.  Ex:  Show a ten frame like this. The top is full so it is 5. Then count on 6, 7.  How many dots? 7
• Notice ordinal positions regarding lines of students or arranging manipulative objects. Ex. “Put the blue bear first, the yellow bear second, and the red bear third.”
• Experience part-whole counting by provide number bond activities such as my favorite, On and Off

4 on and 1 off

• Share stories about counting. Check out this link from The Measured Mom: The Ultimate List of Counting Books
• Develop an observation-type informal assessment checklist to track each child’s ability to do the above.  Assess while they are using math centers or during inside recess opportunities. Here’s a FREEBIE checklist you are welcomed to edit, so I kept it in Word format. Counting Fluency Observation Checklist

Enjoy your counting lessons with your children or students. Use these to identify gaps in students’ concepts. Stay tuned for more development toward understanding of place value.

# More Number Talk Ideas – Part 2

As I mentioned in my last post (More Number Talk Ideas – Part 1), there are many ways to conduct Number Talks with your students. The last post focused on Picture Talks and Which One Doesn’t Belong (WODB). This week I am focusing on Estimation Mysteries and Data Talks.

Esti-Mysteries

Steve Wyborney has been super gracious to share his math estimation mysteries with educators via the nctm.org blog and through his website: https://stevewyborney.com/

What are they?  Each esti-mystery features a clear container with identical small objects (cubes, dice, marbles, manipulatives, etc.). Students estimate how many are in the container, then proceed through 4-5 clues revealed one at a time in a ppt format.  Clues give information dealing with number concepts such as even/odd, less than/greater than, place value, multiples, prime, composite, etc. With each clue, students can then revise their estimate to try to eventually match the actual amount revealed on the last slide. Different clear containers are used with each mystery to include ones with irregular shapes.

It’s really interesting for students to share how they arrived at their estimate, to list possible answers, then defend their choice.  And of course, the rejoicing when/if their estimate matches the revealed amount!

Data Talks

You may have heard of the youcubed website (https://www.youcubed.org) which is partially commanded by well-known Stanford mathemetician Jo Boaler and her co-hort Cathy Williams. You will be amazed at all of the math resources and task ideas for all grades at this site. I witnessed another webinar hosted by these scholars regarding the increased need for data science. While professionals surveyed rarely actually use the algebra, geometry, and calculus learned from high school or college courses, there is definitely an increase in the need for data science / statistics as noted in almost everything we do. So youcubed has made it their mission to ramp up data science resources. One already in the works is “Data Talks” which provides some real-world, interesting, thought-provoking data presentations ready for class discussion.  The link is right here:  https://www.youcubed.org/resource/data-talks/

You will find graphs and tables of all types (some very creative ones), with topics such as these:

• Steph Curry’s shooting and scoring % shown on a basketball court diagram
• Social media use
• Paper towel hoard in 2020
• Dice combinations

Before diving into the data presented, get students to notice first . . . “I noticed . . .”  and follow analysis with “I wonder . . .”  The “I wonder” questions promote ideas about trends and change in data.  Here’s a sample graph regarding possible outcomes when adding 2 dice (graphic from google, not youcubed.org):

Possible noticing and wondering:

• I noticed the graph goes up and then down symmetrically.
• I noticed there are 11 possible sums using 2 dice.
• I noticed the bar for 7 is the highest.
• I noticed numbers on the left side go up by .02 each increment.
• I wonder why 7 is the highest? What are ways to roll a sum of 7?
• I wonder what a graph would look like when actually rolling 2 dice numerous times? Will it be similar to this one?

I highly encourage you to check these out! I will add the sites to my resource list (top bar of my blog) for easy access.

Till next time . . .  Cindy

# More Number Talk Ideas – Part 1

I’m back after taking a couple of months off from blogging! I know some of  you are already back at school, while others will be starting this coming week. I wish the best with all the uncertainties that still lie ahead. BUT most of you are back in the classroom this year, which is a good thing, right?

I am a big advocate of implementing Number Talks as part of a short daily math routine. Most of my previous number talk posts have focused on students sharing strategies for solving problems involving number strings and using known problems to stretch for new problems (such as 3 x 4 and then 30 x 4 or 10 + 8 and then 9 + 8).  Today I would like to start a two-part post about other good quality number talk options which are also designed to elicit critical thinking.

• Picture Talks
• Which One Doesn’t Belong (WODB)

Next post will be these two:

• Esti-Mysteries
• Data Talks

Tips for Implementing:

1. There are multiple ways to interpret, so students can participate at different levels.
2. Project them on a large screen, and allow writing on it to capture the thinking process.
3. A great question to start with is, “What do you notice?”
4. These are great to share with a partner before discussing with the whole group.
5. You may need to assist students with verbally explaining their thinking. Summarize so everyone understands.
6. Relish the chance to introduce or review new vocabulary.
7. Design your own, and have students create some as well.
8. Be amazed at the many different ways to interpret these!

Picture Talks

This involves the use of pictures of objects with the purpose of telling how many and how they were counted (simiar to dot cards, but actual photos of objects arranged in rows, arrays, groups, etc.). A terrific way to practice subitizing, doubles, near doubles, equal groups for multiplication and division, fractions, as well as create story problems with them. Great questions for these picture talks:  How many? How did you see them?

Many of them can be found on google images, but a good resource is via Kristen Acosta.  I participated with her on a recent webinar and was hooked. I have tried many of these with my Zoom online students and they enjoy them because there are multiple ways to analyze a picture to determine how many.

• This is Kristen Acosta’s website. She has posted her photo images free, although you may need to subscribe to access them. She also has other math treasures on her website!  She has a few using egg cartons, which inspired me to go crazy and make my own photos. Feel free to use these below, or take your own! https://kristenacosta.com/number-talk-images/
• Char Forsten is well known in the Singapore Math world. I have had this book for many years and love it! It is great for PreK-2nd grade. What’s inside? Nursery rhymes with pictures that are full of math content. Suggestions for questions to help students notice the pictures to find number bonds. Other photographs you can place under your document camera to project as you discuss. The book is rather expensive, but I found the digit version which is \$15.
• Math Talk by Char Forsten (Digital copy for sale by sis4teachers.org)
• Math Talk by Char Forsten & Torri Richards (Amazon)

Example of different ideas students might have on how to count this:

Which One Doesn’t Belong?

Inspired by the book (or vice-versa), you will see 4 images, numbers, letters, shapes, graphs, etc. To elicit critical thinking, the goal is to have your students select one of the images and tell why it doesn’t belong with the others. BUT, there are many possible responses — as long as the student can explain their reasoning. Follow some of the tips above and have fun exploring all of these free ready-made WODB images!

Image 1 thoughts to get you started:

• Top right because it’s the only one with no holes.
• Top left because it’s the only one with no icing.
• Bottom right: It’s pink and the others all have chocolate

Image 2 thoughts to get you started:

• 9: because it’s the only single digit
• 9: because the other numbers have digits that add up to 7
• 43: because it’s the only prime number
• 16: because it’s the only even number

WODB book at Amazon

WODB designs: Submissions by many, but website created by Mary Bourassa

Which One Doesn’t Belong: 2D shapes from Miss Laidlaw’s Classroom (FREE on TPT)

Which One Doesn’t Belong: 3D shapes from Miss Laidlaw’s Classroom (FREE on TPT)

Which One Doesn’t Belong: 2D shapes for 2nd-7th grades from Jeannie’s Store (FREE on TPT)

Here are more of my egg carton images to get you started!  Please share your experiences with these!

# Multiplication using Ten Frames or Base Ten

Yes, you can even use ten frames to teach multiplication concepts! Here are my mini ten-frames with dot cards from 1 – 10:  Click HERE to get a free copy. These are helpful to use, especially if you don’t have enough tens/ones blocks . . .  or you prefer manipulatives that are slightly easier to manage. These provide a strong connection to place value, and the commutiative and distributive properties.

I recommend two sets of the cards (1-9) per student. Each set has multiple copies of the same number. They can be laminated, cut, and placed in a baggie for ease in handing out and storage.

Multiplication Examples:

1. Single digits (basic facts):
• For the problem 3 x 6, the ten frame is really helpful for the student to see 3 x 6 is almost like 3 x 5 with one more group of 3 added on (by being familiar with the fact that the top row on a ten frame is 5).
• Because of the commutative property, I know these two facts will have the same answer. But which of these below do you think might be “easier” to solve? Students don’t often know they have a choice in how they can use the numbers to their advantage!
2. Double digit x 1 digit:
• Use of these also provides a strong connection of place value and multiplication. Notice how students can see the breakdown on the 4 x 12 problem (4 groups of 12 = 4 x 10 plus 4 x 2). Great introduction to the distributive property of multiplication!
• Here is where application of the commutative property also comes in handy. Which of the methods below would you rather use to solve: count by 4’s or count by 12’s? Again, show students how to use their strengths to decide which way to think about solving the problem.
• Even though the number of total pieces might seem to be a little overwhelming, it definitely is worth the effort for a few lessons so students get a visual picture of the magnitude of the products.
3. Here are other ways to model multiplication problems with manipulatives like base ten rods or base ten disks.

After students get practice using these manipulatives (concrete), then proceed to pictorial models to draw them as simply as possible.  This will give them a good foundation to apply to the abstract (numbers only) problems.  I always pitch for the CPA progression whenever possible!!!

I will pause a while for the summer and just post once a month until school starts up again.  Take care, everyone!  But please don’t be shy.  Post your comments, ask your questions, etc.

# Multiplication strategies — Equal groups

Thanks for checking in on another multiplication strategy! The focus for this post will be on the equal groups strategy — looking at how students can efficiently use this strategy to help learn basic multiplication facts. My angle will be at the conceptual level by using concrete and pictorial methods. Be sure to see the links at the end for books and my free equal groups story cards.

Basics:

• Instead of in array or area format, equal groups are separate groups.
• The “x” means “groups of.”  So 3 x 4 means “3 groups of 4.”

What things normally come in equal groups? Conduct a brainstorming session. I love the book “What Comes in 2’s, 3’s, and 4’s” as a springboard. After reading the book, let students brainstorm other things that come in equal groups. See the pictures below for some more ideas. After some internet research, I also made this attached list to use (in case you or your students draw a blank): click here: Equal groups pictures and list template

Use these lists to help students generate stories about equal groups. When students can create (and maybe illustrate) their own stories, they are much better at solving problems they must read on their own. This also helps students think carefully about what in the story constitutes a “group” and what the “groups of” represents:

1. There were 5 bowling balls on the rack. If you count all of the holes (3 per ball), how many holes are there all together? (5 x 3). The bowling balls are the groups. The holes are what is being counted in each group.
2. How many numbers are shown on 3 clocks? (3 x 12). The clocks are the groups. The numbers are what is being counted in each group.
3. I bought 8 pair of earrings. How many earrings are there? (8 x 2). The pairs are the groups.
4. Seven ladybugs were crawling on the leaves. How many legs would there be? (7 x 6). The ladybugs are the groups. The legs are what is being counted in each group.

Ways to show equal groups with objects and drawings:

• Hula hoops (great to use these in PE class to emphasize multiplication)
• Embroidery hoops
• Circles of yarn
• Dishes:  cup, bowl, plate, tray
• Shelves

Objects to use to show equal groups:

• people
• cubes
• tiles
• mini erasers
• teddy bear manipulatives
• base ten materials
• food: pinto beans, macaroni, cereal, candy
• practically anything you have an abundance of!!

Teaching concepts regarding equal groups:

• When students are placing objects or drawing inside, do they randomly place objects? Or do they organize them to enable ease in counting? Showing students how to organize the objects in each set contributes to their knowledge of equal groups — AND it’s a big help to you as the teacher as you check on students. If the dots are randomly placed, the teacher and student must count one at a time to check. If they are organized, teacher and student can tell at a glance if the amount in each group is correct. Notice the difference below: Which ones show a student’s understanding of 9? Which ones can a student or teacher check rapidly?

• When counting the objects or drawings to determine the product of these equal groups, are students counting one at a time? Or are they counting in equal groups (such as by 2’s, 5’s, 3’s, etc.)? If we allow students to just count by ones, then they are not practicing multiplication . . .just counting!!

Activities to practice equal groups strategy:

1. Circles and Stars:  Roll a dice once. This is the number of circles to draw. Roll a dice again. This is the number of stars to draw inside. If played with a partner, students can keep track of their totals to determine a winner. Dice can be varied depending on the facts that need to be practiced. A spinner can also be used. (See picture at beginning of this post.)
2. Variation of above:  Use other materials (such as those listed above).
• Dice roll #1 = # of cups. Dice roll #2 = number of cubes
• Dice roll #1 = # of hoops. Dice roll #2 = # of pinto beans
• Dice roll #1 = # of plates. Dice roll #2 = # of Cheerios
3. Write and illustrate stories:  Provide a problem for students to illustrate (example:  6 x 3 or 3 x 6).  Then each student can decide how to form the story and illustrate. I always tell students to choose items they like to draw to make their story. Here are some examples.  See some examples from former students.
• There were 6 monsters in the cave.  Each monster had 3 eyeballs. How many eyeballs all together?
• Six princesses lived in the castle. They each had 3 ponies. How many ponies in all?
• There are 3 plants in the garden. They each have 6 flowers. How many flowers are in my garden?
• I made 3 pizzas. Each pizza had 6 slices. How many slices of pizza did I make?
4. PE Class activities:  If your PE teacher likes to help you with your learning objectives, let them know you are working on equal groups strategies. While I’ve not done this personally, I think having relay races related to this would work perfectly. For example, the teacher presents a problem and each team must use hula hoops and objects to show the problem (and the answer).
5. Try these story books about multiplication:
6. Equal groups story problems to solve:  Here are some story problem task cards and templates for solving multiplication and division problems using the equal groups strategy. Click to see the blog post on equal groups story problems and get my FREE set of story problem cards:  HERE

Enjoy!!  Many of you are now off for a well-deserved summer break. Use your summer time to catch up on my postings from this past year, or email me for more information. Also, feel free to comment on any article about your experience or additional tips.

# Multiplication strategies — using arrays

In the last post, I shared my thoughts about multiplication strategies using the repeated addition strategy. This time I will focus on using arrays. Do you have some arrays in your classroom? Look for them with bookshelves, cubbies, windows, rows of desks, floor or ceiling tiles, bricks, pocket charts, etc. Students need to know arrays are everywhere! It is also very helpful for students to build arrays with objects as well as draw them. This assists students with moving from concrete to pictorial representations — then the abstract (numbers only) can be conceptualized and visualized more easily. Some good materials for arrays:

• cubes
• tiles
• circular disks
• flat stones
• pinto beans (dry)
• grid or graph paper
• bingo stamper (to stamp arrays inside grids)
• mini stickers
• candy (Skittles, M&Ms, jellybeans)

Array Basics:

1. Arrays form rectangular shapes.
2. Arrays are arranged in horizontal rows and vertical columns.  This vocabulary is very important!
3. The number of objects in each row (and column) in an array are equal.
4. Arrays can be formed by objects, pictures, or numbers.
5. Arrays can be described using numbers:  If there are 4 rows and 3 columns, it is a 4 by 3 array.
6. The number of rows and number in each row are the factors. The product is the total.
7. When an array is rotated, this shows the commutative property.

Ways to incorporate arrays into story problems:

• Desks in a class (5 rows, 4 desks in each row)
• Chairs in a classroom or auditorium (10 rows of chairs, 8 chairs in each row)
• Plants in a garden (6 rows of corn, 8 corn plants in each row)
• Boxes in a warehouse (7 stacks, 5 boxes in each stack)
• Pancakes (3 stacks, 5 pancakes in each stack)
• Cars in a parking lot (4 rows, 5 cars in each row)
• Bottles of water in a crate (3 rows, 8 bottles in each row)
• Donuts or cupcakes in a box (how many rows? how many in each row)

Activities to encourage concrete and pictorial construction of arrays:

• Start off using manilla grid paper you probably have available with the construction paper supply at your school. This will help students keep their rows and columns even. Pose a problem and allow students to use manipulatives you have available to construct the array.  If you say, “Build an array for this multiplication problem: 3 x 5,” do they know the 3 refers to # of rows and the 5 refers to the number in each row?  Starting off using this graph paper may help when students freehand their own array (to help keep rows and columns lined up and not going astray).
• Turn the paper after building the above array to see the commutative property. Now the picture shows 5 x 3 (5 rows with 3 in each row). The product is still 15.
• Use the manilla grid paper along with bingo dobbers to create the array.  The grids can also be completed with mini stickers (I get them all the time in junk mail) or drawings.
• When using pictures of arrays, direct your students to always label 2 sides of the array (the rows and columns). Try to label different sides of the array so it’s not always presented in the same format.
• Find the product:  The whole point of using an array as a multiplication strategy is to visualize the rows and columns to help calculate the product. If students create rows and columns and then just count the objects one-by-one, then this does not accomplish the objective.  Show students how to skip count using the # of objects in the rows or columns. Believe me, students don’t always know to do this without a hint from the teacher.  Or better yet, before actually telling them to do this, ask students this question: “How did you get the total number of objects?” When you pose this question, you are honoring their strategy while secretly performing an informal assessment. Then when the student who skip counted to find the total shares their strategy, you give them the credit:  “That is an efficient and fast way to count the objects, thank you for sharing! I’d be interested to see if more of you would try that with the next problem.” Plus now students have 2 strategies.
• Use the distributive property to find the product: Let’s suppose the array was 6 x 7.  Maybe your students are trying to count by 6’s or 7’s to be more efficient – but the problem is that counting by 6’s or 7’s is difficult for most students. Break up (decompose) the array into smaller sections in which the student can use their multiplication skills.  Decomposing into rows or columns of 2’s and 5’s would be a good place to start. This is the distributive property in action – and now the students have 3 strategies for using an array!! This is a great way to use known facts to help with those being learned.Here is a link to Math Coach’s Corner (image credited above) and a great array resource: Multiplication arrays activities from TPT \$5.50.  Here is my FREE guided teaching activity to help students decompose an array into 2 smaller rectangles. Click HERE for the free blank template.
• Use the online geoboard I described in a previous post to create arrays using geobands. Click here for the link: Online geoboard  Click here for the previous post: Geometry websites (blog post)
• Try these freebies:  Free array activities from k-5mathteachingresources.com. Here’s a sample.

• Play this game I call “Block-It.” This is a competitive partner game in which students must create arrays on grid paper. Click here for a FREE copy of the directions: Block-It Game Directions
• Relate use of arrays when learning strategies for division and area.

In a future post I will show some ways to use manipulatives and pictures arrays for double digit multiplication problems. Stay tuned!!

The next few posts will continue to focus on the basic multiplication concepts one at a time. This will allow the opportunity to dig deeper into the concepts we want students to understand. This one will focus on the concept that multiplication is repeated addition. These posts will be helpful to teachers introducing multiplication to students in 2nd and 3rd grade as well as those in 4th, 5th, 6th and beyond who have missed some of these basic concepts. Future posts will focus on the area (array), set (equal groups), counting, decomposing, and doubling/halving models as well as the associative and distributive properties.  Freebies below!!

Do your students know what the “times” sign means? They may hear it frequently, but not realize what it means. I like to interpret it as “groups of.”  So a problem like 3 x 4 can be said as “3 groups of 4.”

To show repeated addition, that same problem would be 4 + 4 + 4 = 12.

Repeated addition can be shown with numbers, and also with arrays and equal groups. These pictorial models are great for developing multiplication concepts (and will be topics of future posts). However, when students are presented with these models they often count the individual pieces one at a time rather than adding the same amount repeatedly. Observe your students to see how they are counting. . . and encourage counting in equal groups to promote a growth of the multiplication mindset.

Do your students apply the commutative property of multiplication? This means if the problem is 3 x 4, it can also be solved by thinking of 4 x 3 (which is 4 groups of 3 OR  3 + 3 + 3 + 3). I want students to know even though the answers are the same, the way the factors are grouped is different. When used in a story, 3 x 4 is a different scenario than 4 x 3.

Do your students practice repeated addition, by combining 2 or more numbers? See the following for an illustration of 15 x 6:

Do your students apply the concept of repeated addition to multiple digit multiplication problems as well? I have witnessed students numerous times who only try a problem one way and struggle. For example, on a timed test I witnessed a 5th grader attempt the problem 12 x 3. I observed him counting by 3’s.  He was trying to keep track of this by skip counting by 3’s twelve times (using his fingers). I could tell he had to start over frequently, thus spending a lot of time on this one problem. It became obvious he had no other strategy to try. He finally left it blank and went on. Just think if he had thought of 12 + 12 + 12. This should have been relatively easy for a 5th grader.  He also could have decomposed it to this: (3 x 2) + (3 x 10).

Do your students always go to the standard algorithm when they could perhaps mentally solve the problem by repeated addition? If the problem was 50 x 3, are they thinking 50 + 50 + 50? Or are they using paper-pencil and following the steps?

What about a problem such as 45 x 4?  Using repeated addition, is your student thinking of 40 + 40 + 40 + 40 combined with 5 + 5 + 5 + 5? This is then solved as 160 + 20 = 180.

Here are a few resources (FREE) that might help with this strategy:

Students who are able to use repeated addition skillfully are showing a healthy understanding of place value and multiplication. This strategy also enhances mental math capabilities. Conducting daily number talks are highly advised as a way to discuss multiple ways to solve a given problem such as those mentioned above. Check out “Number Talks” in my category list for more information on this. Also check out some recommended videos about conducting number talks (above black bar “Instructional Resources”).

# Multiplication — Developing an understanding

Are you looking for some ways to help your students learn the multiplication facts? Or ways to help them solve multiplication problems while they are in the process of learning the facts? One way is to skip count or repeatedly add the number over and over again. While this is one acceptable strategy, I see many students skip count using their fingers, often starting over numerous times. And if the child miscounts just one number in the sequence, then all of the remaining multiples/products are incorrect. Sometimes the student will write down the sequence in a horizontal row (better than using fingers in my opinion), but again – if they miss one number . . . all the rest of the numbers in their list are wrong.

What I want to show you today (in Part I of my series about multiplication strategies) are ways to relate the multiples/products in recognizable patterns which may facilitate recall and help with committing the facts to memory. Yes, students should also know the following about multiplication – and I will focus on all of these in future articles:

1. Multiplication is repeated addition. For example: 3 x 4 means 3 groups of 4 or 4 + 4 + 4 = 12
2. Multiplication is equal groups. 3 x 4 might be shown with 3 circles and 4 dots in each one. Be cautious about continued use of this one. Students are good at drawing this out, but then are they actually adding repeated groups or just counting one dot at a time. Observe students to see what they are doing. Transition to showing 3 circles with the number 4 in each one.
3. Multiplication is commutative. If solving 7 x 2 (7 groups of 2), does the student count by 2’s seven times, or perhaps make it more efficient by changing it around to make it 2 x 7 (2 groups of 7 — and adding 7 + 7)?
4. Multiplication can be shown with arrays. If students are drawing arrays to help solve, watch how they are computing the product. Are they counting one dot at a time? Or are they grouping some rows or columns together to make this method more efficient. I will focus on this one in Part 2.
5. Multiplication facts have interesting relationships — stay tuned for future posts or check out my blog archives for more
• An even number x an even number = an even number
• An odd number x an even number = an even number
• An odd number x an odd number = an odd number
• 2’s, 4’s, and 8’s are related
• 5’s and 10’s are related
• 3’s, 6’s, and 9’s are related
6. Multiplication can be shown by skip counting.  Aside from my comments above about errors students make with skip counting, there are some ways to arrange skip counted numbers in distinctive organized groupings so the patterns become more noticeable, perhaps leading more to memorization than just a horizontal list of numbers, or using fingers.
• I have included 2 visuals to see some of my favorite ways to relate skip counting to unique patterns (for the 2’s, 3’s, 4’s, 6’s, 8’s, and 9’s). Visualizing and explaining the patterns is a good exercise for the brain.  Can your students come up with another way to visualize the patterns with these numbers?

Stay tuned for more blog entries about multiplication!

# Building a Classroom Community – Learning Names and Other Teamwork Activities

Since many of you may just now be coming back together with your students in person due to hybrid or virtual teaching models, I thought I’d revise this post I wrote 3 years ago concerning establishment of a classroom community.  While you may feel extra pressure to get back into some serious catch-up learning lessons, time spent on creating a genuine classroom community is definitely worth it and should pay off.

Creating a sense of community within your classroom puts emphasis on establishing a climate of mutual respect, collaboration, kindness, a positive atmosphere, and a feeling that each one is a valued member of the class. This is also critical to help you prepare for small group collaborative practices for your reading and math instructional program. See the freebie of fun teamwork activities in the last paragraph!

There are many ways to accomplish this, of course. But I will share my favorites. Before Great Expectations came to SW Oklahoma, I became familiar with an organization called Responsive Classroom (click to link to their website). They are similar to GE, but primarily train teachers in the NE part of the U.S.  Like GE, they also focus on a strong link between academic success and social-emotional learning. You can subscribe to their newsletter and order wonderful books via their website. I started with one of their books called “The Morning Meeting Book” (click on title). It promotes ways to create a classroom community by having a daily “Morning Meeting.”

In my classroom, we formed a circle every morning and greeted each other by name in fun ways. See some ideas below in the bulleted section.  You might be surprised to know that students often don’t know their classmates names, even after several weeks of school! Knowing and using a child’s name is a sign of respect. Through this circle, we also shared successes and concerns for one another, began discussion topics about how we should behave and respect one another, welcomed new students, made group decisions, and set the tone for the day. Every student was acknowledged and felt valued every day. Students don’t want to disappoint a teacher or classmate they respect, and it almost eliminated the need for time consuming behavior plans.  For a great plan to get students in a circle in a timely manner see Activity #22 in the Teamwork Activities linked below (last paragraph)

Name Greetings:

• One student starts. Student #1 offers a type of handshake to the person to their right -Student #2 (handshake, pinky shake, salute, wave, high five, fist bump), and says, “Good Morning, ________ (name).” Student #2 returns the greeting (also with eye contact), “Good morning, ________.” Then Student #2 greets Student #3, and it goes all the way around the circle.  I usually only introduce one type of hand gesture at a time. After we learn all of them, then I often give them a choice. I have to teach eye contact, sincerity, how to give a proper handshake, and what to do if you don’t know/remember their name.
• After we have mastered the above, I introduce some other way to greet. One is to write each student’s name on an index card and place the stack face down in the middle of the circle. Turn over the top 2 names and they greet each other. Keep turning over 2 names at a time until the whole stack is completed.
• Learn a greeting in another language (such as Hola or Buenos Dias, Guten Morgen, Bonjour, etc.).
• Using a ball, student #1 rolls it to a student across the circle to greet them (student #2). Then student #2 rolls the ball across the circle to greet #3, and so on.
• If we are crunched for time, we shake to the left, shake to the right, say “Good Morning, ____” and are all done!!

Teamwork Activities:

Through my years of GE training, I added teamwork activities to our classroom routines – especially at the beginning of the year. And then we continued them once a week because caring has to be practiced. We loved “People to People” and “Black Socks” and the “Woo Game.” I am attaching a pdf of  22 Movement, teamwork, energizer activities – I hope you will try some. Many of them require no advance preparation. I feel taking the time to create a caring atmosphere was worth every minute. When students have the opportunity to engage in fun activities together and learn their names and interests, they are more likely to show genuine respect toward one another.

# Interactive math lessons and activities on NCTM

Resource – http://illuminations.nctm.org

This is a math resource I absolutely love! It is a product of the National Council for the Teachers of Mathematics (NCTM).

This site includes lesson plans and interactive activities. Search in several ways: by topic, by standard, or by grade level. Need some strategy games? Check out “Calculation Nation” (some of which can be played against other players), and “Brain Teasers.” I have just added this link to my Resources page (on my blog home page).  Pass this along to parents for them to use with their children at home!

Many of the lessons connect to exploration projects and literature. The interactive features are outstanding!! These are perfect for the smartboard, on laptops, or tablets. Doing Zoom lessons? Then these are also wonderful for sharing the screen to introduce or review concepts. Once you are on the home screen, click the Interactives box (right side) and then the desired grade level. There are dozens of great applets, but here are a few you might really like. I have linked them for easy reference, so just click on the  title and you’ll be there:

Dynamic Paper: Customize graph paper, number lines, spinners, nets, number grids, shapes (to include pattern blocks, color tiles, and attribute blocks), and tessellations. You can also choose inches or cm. These can be customized, saved and printed as jpeg or pdf. I created the spinner shown here from this application.

Five Frame and Ten Frame tools: Geat activities to build number sense using five or ten frames. These may take 1-2 minutes to load.

Cubes: Build a rectangular prism one cube, or row, or layer at a time and then compute the volume or surface area.

Coin Box: Drag and exchange coins. There is also a feature I like (the grid at the bottom right corner), which puts coins in blocks (by 1s for pennies, 5s for nickels, 10s for dimes, and 25s for quarters). This really helps see the value of the coins. Want more info about coin blocks? Once on the Coin Box page, click on the “Related Resources” tab.

Try these for fractions: Fraction Models (which includes decimal and percent equivalencies) and the Fraction Game.

Geometric Solids: Create a shape (either transparent or solid) and swivel it around to see all of the faces, vertices, and edges. It has a cube and pyramid as far as basic 3D shapes are concerned. I wish it had more that 3rd-5th students would encounter.

Here’s a nice multiplication game:   Two players (or a player vs. the computer) choose factors from the bottom bar to create products shown on the game board grid to get 4 in a row (and try to block your opponent from getting 4 in a row).  Be sure to see the directions included.

Some of the interactives require an NCTM subscription.  The ones I have listed above should be okay to access without membership. I have subscribed for years and just paid \$94 for this coming year. Well worth it if you plan on using their site extensively.  This subscription also entitles you to a print and and online journal, blog capabilities, and more.

Enjoy these and so many more!!! Let us know if there are others you recommend.  I’ll highlight more on my next post.

# Sight Word Activities

This post contains some of my favorite sight word activities and resources to help your students practice those sight words and high frequency words.  If you haven’t read part 1 (Sight word instructional tips), be sure to do that as it contains information about research based teaching strategies. These all focus on ways for the child to actually read / say the word and use in a sentence, not merely matching, copying, or building the word. Here goes!!

1. Sight word tic-tac-toe:
• Played with partners or teacher vs. students
• Materials needed:  tic-tac-toe template on a small whiteboard or on a laminated page
• Two-color counters so each student can mark their spot
• Select 9 sight words you would like to review.  Have students write them in randomly in the 9 tic-tac-toe spaces
• Each player selects a word to read.  If read correctly, they can put their counter on the space.  You may also require students to use the word in a sentence.
• 3 in a row wins the game. Then play again!
• You may choose to give corrective feedback regarding missed words:  Example:  “No, this word is ________. You say it.”
2. Sight word sentence cards:

• Using the words in sentences (or phrases) helps students put the word into context.
• Try these sight word cards from a blogger I follow (www.thisreadingmama.com).  If you subscribe to her blog, you will find these and dozens of other good reading resources for free. Check out: Sight Word Cards with Sentences (Link to free resources)
• I mentioned this in the last post, but a great research-based method for using these with individual students is to select no more than 10 words. Show the word. If it is known, put it in a separate pile. If it is unknown or the child is hesitant or guesses, tell the child the word, read the sentence so they can hear it in context, have the child say the word, then put the card 2-3 spaces back in the pile so they will see it again in a short amount of time. Repeat with other cards.
3. Sight word teaching routine:
• Please take a look at this KG teacher’s routine for teaching and practicing sight words.  It is called “Sight Word 60” because through this routine, students get a chance to hear and use the word 60 times during the week. Sight Word 60 by Greg Smedly-WarrenLook for videos for each day, plus center and celebration activities. This routine can also be followed in 1st and 2nd grade classes or small groups.  Especially good for use with tutors, paraprofessionals, or volunteers!
4. Sight word path game:
• This simple path game scenario is well-researched. You are likely to find several versions available. Here is mine (also pictured below): Reading Race Track for Sight Words CE   In part 1 (last post), I linked one from another popular blogger (Playdough to Plato). Here is another editable one from Iowa Reading Research: Reading Race Track (editable).
• Teacher fills in the words being practiced (5-7 words repeated 4x each placed randomly).
• The track can be used by students for practice (they can roll a die, move to the space, pronounce the word, and perhaps use it in a sentence).
• The track can be used by teachers and students for timed practice after they have been introduced. A recording sheet is included with my version as well as the Iowa version.

Page 2 of Reading Race Track by C.E.

5. Sight words in context:
• Of course students benefit from practicing sight words in context.  In your guided reading group, allow students to use mini magnifying glasses (check the dollar stores) or those fancy finger nails that slip over a finger to locate sight words you call out. Example:  “Find the word said on this page.  Can you find it on another page?  Read the sentence it is in to your partner.”
• My favorite way to practice sight words in context is through short, fun poetry. Here is a great resource (sorry, it’s not free) full of poems which target specific sight words. I’m sure there are others out there – let us know of ones you have found!  Sight Words Poems for Shared Reading by Crystal McGinnis (TPT for \$4.00)
6. SWAT!
• Find some new flyswatters.  If you are working with a small group, you just need 2.
• Lay out 4-8 sight words you are working on (table top or floor). You could also write them on the board. Teacher calls out a word.
• The object is for the students to locate and hold their swatter on the word you call out.
• The student who found it first will have their swatter under the second student’s swatter — proof of who found it first.
• This is also great for other vocabulary practice or math facts!!

Find the word “said”

7. Memory / Concentration:
• Make 2 copies of each sight word on index size cards. You might limit to 8 cards for KG students and 12 cards for 1st or 2nd.
• Arrange the cards in a rectangular array.
• First player selects 2 cards to turn over and read. If they are a match, they can keep them.
• STRESS to students to just turn the cards over and leave them down — don’t pick them up. This is because the other students are trying to remember where these are located – and they need to be able to see them and their location. It’s a brain thing!!

Notice that in all of these methods, the students need to read and say the word (and perhaps use it in a sentence). Be sure your sight word activities reinforce these. Activities in which students just merely match, stamp, copy, write in different colors, recreate with letter tiles, etc. do very little to help them really know the word. Have FUN!!!

What other sight word activities have you tried that you’d like to share? Take care, friends!

# Sight Words Instructional Tips

Sight words are those which students can identify automatically without the need to decode. They often do not follow phonics “rules.” Examples: who, all, you, of. They may include some high frequency words (HFW). High frequency words are those which occur most often in reading and writing. By learning 100 of the HFW, a beginning reader can access about 50% of text.  According to Fry, these 13 words account for 25% of words in print:  a, and, for, he, is, in, it, of, that, the, to, was, you.

When are students ready to learn sight words?  According to the experts from Words Their Way (Bear, Invernizzi, Templeton), student need to have a more fully developed concept of word.  Concept of Word is the ability to track a memorized text without getting off track, even on a 2-syllable word. In other words, does the child have a one-to-one correspondence with words? When tracking, does their finger stay under a 2-syllable word until it is finished, or are they moving from word-to-word based on the syllable sounds they hear? In the sentence shown, does a student move their finger to the next word after saying ap- or do they stay on the whole word apple before moving on? Students in the early Letter-Name Stage (ages 4-6) start to understand this concept. It becomes more fully developed mid to later stages of Letter Names (ages 5-8).

Students with a basic concept of word are able to acquire a few words from familiar stories and text they have “read” several times or memorized. Students with a full concept of word can finger point read accurately and can correct themselves if they get off track. They can find words in text. Therefore, many sight words are acquired after several rereadings of familiar text.

1. To help children gain concept of word:

• Point to words as you read text to them (big books, poetry on charts, etc.).
• Invite children to point to words.
• Pair memorized short poems with matching word cards for students to reconstruct. Using a pocket chart is helpful.

2. Explicit Instruction: Dedicated time each day for sight word work

• KG: 1-3 words per week; 1st grade: 3-5 words per week
• Introduce with “fanfare and pageantry”.
• Read, chant, sing, spell, write.
• Use them in a sentence and ask children to do the same.
• Use letter tiles, magnetic letters, word cards.
• Use with a word wall (see more info later in this post).
• Locate in text you are reading (poems, big books, stories in small group).

a box of juice

• Many sight words are hard to explain the meaning (the, was, of). Associate with a picture and phrase or sentence such as: a box of juice.
• Reinforce with small group instruction.
• Practice at learning stations:  CAUTION — activities should be done with previously learned  words to promote fluency. If the words are not known, then stamping them in playdough or writing them multiple times may not help you achieve your objective. Saying them correctly along with visual recognition is key. Go to this blogger’s link for many free resources for reinforcing sight words.  http://www.playdoughtoplato.com/pirate-sight-word-game/   She has a simple path board game which is editable. You can put in 1-5 sight words to practice – students must say the word to their partner to advance along the path. I often require students to use the word in a sentence as well. She is a great resource for KG-2nd grade!!
• I (and experts) do not recommend using sight words on weekly spelling lists. Research suggests  spelling words should follow typical orthographic patterns, which many sight words do not have (ex: who, was, all, of). If you practice sight words in ways mentioned above, students will get better at spelling them or can refer to the word wall when needed for writing assignments.

3. Flash Card Practice (Research based method) with no more than 10 words: Continue reading