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:
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:
Have a terrific week! Happy measuring!
]]>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.
Advantages:
Virtual Manipulative Links
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.
]]>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.
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:
CVC: Consonant-vowel-consonant words
CVCE: Consonant-vowel-consonant + silent e
Long vowel teams: Generally this means 2 vowels together making just one sound
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:
Have a wonderful week everyone!
]]>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:
Miscellaneous parent involvement tips:
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:
In-person volunteers:
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.
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! Here are a few links to some of my previous posts regarding teamwork, student engagement, literacy and math. You might be interested in these to help start your journey this year. And in case you didn’t see it, I have an easy link to most of my own free resources. Click here to get it now, but it is also available in the black bar above. Have a great start to your year and Enjoy!!! Please invite some of your new teachers to check out my blog! Also check the categories list on the website (side bar if using a monitor, bottom of the webpage if using a phone). The search bar might also help you with what you are looking for. Have a great start to your year!!
Some other tips to get prepared for your literacy lessons:
General welcome back tips:
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.
For the boxed area model, break up the factors by place value. If multiplying with a one-digit number, you only need 1 row. If multiplying 2 digits by 2 digits, you need 2 rows. 3 digit by 2 digit would need 3 columns and 2 rows. Then multiply each part together and add the partial products. For double digits, the adding can be done vertically or horizontally (using mental math).
With this model, students get to practice multiplying by groups of 10. As shown: 60 x 3 . . . think of 6 x 3 = 18, then multiply by 10 (add a zero) to get 180. For 60 x 30, think of 6 x 3 = 18, then multiply by 100 (add 2 zeroes) to get 1800.
Partial Products: This model produces the same partial products as the area model, but in a more algorithmic looking format (vertically). Students take apart the factors, but instead of combining multiplication with regrouping / adding within the problem, all of the products are listed below, lined up in columns of course. Again, this method helps students think of what each part of the multiplication problem means, with heavy emphasis on place value and realizing that in the problem 65 x 3, it’s not 6 x 3 but 60 x 3. For students, using lined notebook paper turned sideways helps keep columns lined up – or graph paper helps too. Examples:
Bowtie / F.O.I.L. Method: In case you have seen this model ciruculated on Pinterest, you will see the same information as the area model and partial products, but the visual of the lines on the bowtie might help make sure all factors are multiplied. Break apart the factors by place value and put one across the top and the other across the bottom. Then start at one corner, follow the lines, and multiply the two numbers at each end of the line together. Stop when you get back to where you started. Add all of the products together.
The F.O.I.L. method is a term students will hear more in algebra regarding multiplying binomials, but it applies when multiplying two double-digit numbers together also. F = First (multiply the first two numbers in each set of numbers); O = Outside (multiply the two outside numbers); I = Inside (multiply the two inside numbers); and L = Last (multiply the last two digits, which are the ones).
Have a great week!! Next post will be place value regarding division.
Interested in tutoring individual or small groups of students? You may be interested in Varsity Tutors. You can choose your hours and the students you would like to work with. See the link with my picture. If you are interested, use this link and each of us gets a little bonus!
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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:
Addition and Subtraction:
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!!
]]>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.
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:
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:
Partitioning:
Relationships:
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.
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!
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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?
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:
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?
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.
]]>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:
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 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
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