# First Day Math & Literature Activity K- 5

The book, Chrysanthemum, by Kevin Henkes is one my my all time favorite first-day-of-school stories to share with my students – no matter what grade level. The main character is Chrysanthemum, who is all excited about her first day of school until the other students start making fun of her name because it is soooo long. This makes her reluctant to go to school until everyone finds out their favorite music teacher has a long name (Delphinium) and is planning to name her new baby Chrysanthemum. A poignant story to help children develop a sense of empathy and compassion and realize that everyone’s name is special – no matter what it is or how long or short it is!

• Letter and name recognition
• Counting letters in names
• Name graph with a variety of methods (paper graph, color tile or unifix cube graph, etc.)
• Name grid art activity (see below)
• Comparing name lengths

• Name graph – can use first, middle, and/or last names. To start, just have students write their name on a post-it-note and stick it on the board. Then rearrange into columns or rows according to how you are collecting your data. Or make a frequency table, line plot, percentage pie chart, etc.
• Name grid art activity (see below). Review terms: row, column, grid, array.
• Use some type of strategy to determine total number of letters in first names in the class (repeated addition, multiplication). Using the example graph, students could add 3 + (4 x 5) + (5 x 8), and so on. Let students think of the strategy though!
• Determine most often and least often used letters.
• Determine the mean, median, mode, and range using length of names.

Name grid art activity Continue reading

# Number Lines and Rounding

I get requests from many teachers to help with instructional strategies regarding rounding, so I am happy to share my thoughts (and freebies) with you. Difficulty with rounding usually means students lack number sense. The essential goal of rounding is: Can you name a benchmark number (whole, tens, hundreds, thousands, tenths, hundredths, etc.) that a given number is closer to? I have found the more experience a student has with number lines, the better they will be with number sense, and the better they are with rounding to the nearest ___.  Then this rounding practice must be applied to real world problems to estimate sums, differences, products, or quotients.

When doing a google search for tips on rounding (ie Pinterest), you very often find an assortment of rhymes (such as “5 or more let it soar, 4 or less let it rest”) and graphics showing underlining of digits and arrows pointing to other digits. These steps are supposed to help children think about how to change (or round) a number to one with a zero. Many students can recite the rhyme, but then misunderstand the intent, often applying the steps to the wrong digit, showing they really don’t have number sense but are just trying to follow steps.

My answer (and that of other math specialists) is teaching students how to place any number on a number line, and then determining which benchmark number it is closest to. Continue reading to see examples and get some free activities.

# Multiplication Strategies Part 5: All Strategies Combined PDF

One of my subscribers really liked the multiplication strategies I posted in my 4 part series, but was finding it difficult to copy them for easy reference. So . . . I pooled pictures of the boards onto a single PDF (it’s 10 pages) and am providing it here (and also with the 4th part of the series). Click here for your copy: Multiplication Strategies PDF

Enjoy!!

# Multiplication Strategies Part 4: Doubling and Halving (and Lattice)

Doubling and . . .

I hope you have had a chance to look at Parts 1, 2, and 3 of my multiplication strategy posts. These strategies are especially helpful with 3rd – 5th grade students (and beyond). I have been reading a book by Dr. Nicki Newton called “Guided Math in Action.” She discusses five components to being mathematically proficient. One of them is strategic competence.  What is strategic competence? The National Research Council defines it as “the ability to formulate mathematical problems, represent them, and solve them.” The first process std. in Common Core (Make Sense of Problems and Persevere in Solving Them) emphasizes strategic competence in this way: “they try special cases and simpler

Halving Multip. Strategy

forms of the original problem in order to gain insight into its solution, . . . students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? . . . and, they can understand the approaches of others to solving complex problems and identify correspondences between different approaches.”

With all of that said, I would like to show two other multiplication strategies: 1) Doubling and Halving, and 2) the Lattice Method. All of the strategies picture boards I have shown are available on this free PDF (It’s 10 pages): Multiplication Strategies PDF

Doubling and Halving
Doubling and halving is supported by the associative property. It also enables the student to use mental math strategies. Here is an example:  Original Problem: 25 x 12.  When changed to 50 x 6, I can solve it mentally which equals 300.  From what I have researched and applied, here are some tips:

• Use when a problem has one even and one odd factor (or two even factors).  It won’t work with 2 odd factors because you can’t break an odd number in half and still get a whole number.
• Double the odd factor and halve the even factor. Do this 1-3 times until you get two factors which can be multiplied mentally.
• Most useful when the odd factor has a 5 in the one’s place (because 5 doubled is 10, so the result will be a multiple of 10 which can usually be taken care of mentally).

How is the above problem connected to the associative property?

• Think of 25 x12 as 25 x (2 x 6).
• If I apply the associative property, I get (25 x 2) x 6 = 50 x 6 = 300.
• I can also go another step further and show that 50 x 6 = 50 x (2 x 3) = (50 x 2) x 3 = 100 x 3 = 300.
• Here is another one: Think of 15 x 24 as 15 x (2 x 12) = (15 x 2) x 12 = 30 x 12 = 360.
• See my pictures below of how that looks in array form with the problems 3 x 4 and 5 x 12.

# Eureka Math Blog

I just found this blog for Eureka Math. It has ten very good topics to explore, especially for Lawton, OK users who will likely be directed to the Eureka Math curriculum (also known as EngageNY).  Plenty of good advice for new users. Put it on your list for the summer!!! Click below to get there fast!

https://greatminds.org/math/blog/eureka

I will also add this to my resources list.

Enjoy!  Cindy Elkins

# Multiplication Strategies Part 3: Connecting to Place Value

In  Multiplication, Part 3  I will focus on 3 strategies for double digit numbers:  area model, partial products, and the bowtie method. Please also refer back to my Dec. 6th post on Number Talks for 3rd-5th grade where I mentioned these and other basic strategies for multiplication. 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 and 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. Try my “Choose 3 Ways” work mat as bell work or ticket in the door. Get it free here.

Area Model: This method can be illustrated with base ten manipulatives for a concrete experience. Remember the best methods for student learning (CPA) progresses from concrete (manipulatives) to pictorial (drawings, templates, pictures) to abstract (numbers only). 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

# Multiplication Strategies Part 2: Decomposing and distributive property to learn facts

In part 2, I will show you some ways to help students decompose a multiplication problem into 2 (or more) easier multiplication problems. Most students know problems with factors of 2, 5, and 10. The decomposing will allow students to use what they know to work on the unknown / unmemorized fact.

I frequently see students struggle with solving an unknown multiplication problem. Often they choose skip counting, but if they miss just one number in the sequence, the answer comes out wrong. I also see them use their multiplication chart, but this doesn’t do much to help them apply number sense. Other times I see students draw circles with dots inside, but this is time consuming and it often becomes just a counting practice. This method is using the distributive property. Students can break apart one of the factors into “friendly” addends. I usually advise making one of the addends a 2, 5, or 10 since those are usually easier to compute or are already memorized. Here are some examples:

I have also attached a class activity sheet in which students cut out grids, glue them on the worksheet and then decompose them. Get it free here: Distributive property teaching chart  Another resource for teachers is my multiplication strategies guide which shows some ways to break down each factor’s family. Get it here free: Multiplication fact strategies chart  Finally, here is a link to a TPT source with a freebie for using the distributive property with arrays: Distrib. Property of Multip. freebie by Tonya’s Treats for Teachers

Have a great Spring Break for Oklahoma teachers!! I will be back in 2 weeks with more multiplication strategies.

# Multiplication Strategies Part 1: Basic Strategies and skip counting

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:

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 can be shown by skip counting.

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? Here’s another pattern below:

• 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

Next post will be Part 2 of Multiplication Strategies. Have a great week!

# New OK Math Framework

At last, some help with regard to organization and implementation of the new math OAS (Oklahoma Academic Standards) has arrived!!!!

The OK State Dept. of Education (via their directors of elementary and secondary math) has assembled a great team of math minded teachers and experts to put together a framework of the newly adopted math standards for Oklahoma. Here is the link: OK Math Framework. Look for the following features:

• Introduction video (short) – on the lower right side of home page
• Action and Process Standards
• Suggested Learning Progression
• Objective Analysis

Suggested Learning Progression: This is partitioned off into units, suggested timeline, and objectives. Each unit is presented as a bundle of linked objectives. Many objectives are repeated throughout the year, while some objectives are split so that part of the objective is taught in one unit and completed in a later unit (shown by strikethroughs). Makes so much sense!!! Clicking on the title of the unit (ex: Place Value) will take you to another view with sample tasks.

Objective Analysis: Click on any objective number (ex: 1.N.1.4) and you will see a more detailed explanation of the objective, along with student actions, teacher actions, key understandings, and common misconceptions. Continue reading

# Illuminations NCTM Interactives

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).

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. 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.

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.

Equivalent Fractions: Build different fractions in circular or rectangular format. Compare them and see them on a number line. You can manipulate the numerators and denominators to see fractions change right before your eyes! Others 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.

For your graphing needs, check out the Bar Grapher, Circle Grapher, and Data Grapher. With these tools you can create graphs using any of your own data. Some of these need Java installed.

Enjoy these and so many more!!! Let us know if there are others you recommend.

# Number Talks Part 3: Computational Strategies 3rd-5th grades

This is the Part 3 of Number Talks. If you are just tuning in, please refer to NT Parts 1 and 2. As I mentioned before, conducting a Number Talk session with your students is a chance for them to explain different ways to solve the same problem. This is meant to highlight strategies which have already been taught.

Click below to watch  2 videos of how to conduct a Number Talk session with intermediate students. You will see many strategies being used.

Number Talk 3rd grade 90-59 = ____

Number Talk 5th grade 12 x 15 = ___

Addition and Subtraction Strategies:  I like using the methods listed below before teaching the standard algorithm. This is because they build on a solid knowledge of place value (and number bonds 1-10). If your students are adding and subtracting using the standard algorithm and can’t adequately explain the meaning of the regrouping process in terms of place value, then try one of the following methods. In many cases, I will ask a student the meaning of the “1” that has been “carried” over in double-digit addition. About 85% of the time, the student cannot explain that the “1” represents a group of 10. When adding the tens’ column, they often forget they are adding groups of 10 and not single digits. So they get caught up in the steps and don’t always think about the magnitude of the number (which is part of number sense). You will notice teachers write the problems horizontally in order to elicit the most strategies possible.

• Partial Sums
• Place Value Decomposition
• Expanded Notation
• Compensation
• Open Number Line (to add or subtract)

Here are some possible Number Talk problems and solutions:

Multiplication and Division Strategies: I like using these methods before teaching the standard algorithms. Again, they build a solid understanding of place value, the use of the distributive property, and how knowledge of doubling and halving increases the ability to compute problems mentally. Once these methods have been learned, then it is easy to explain the steps in the standard algorithm.

• Area Model
• Partial Products
• Distributive Property
• Doubling and Halving
• Partial Quotients

Here are some possible Number Talk problems and solutions:

# Number Talks Part 2: Strategies and decomposing with 1st-3rd grade

For 1st -3rd grade students: Refer to “Number Talks Part I” (posted Nov. 12, 2016) for ways to conduct a Number Talk with KG and early 1st grade students (focusing on subitizing and number bonds). For students in 1st – 3rd grade, place extra emphasis on number bonds of 10.

Write a problem on the board, easel, or chart tablet with students sitting nearby to allow for focused discussion. Have the following available for reference and support: ten frame, part-part-whole template, base ten manipulatives, and a 0-100 chart. Present addition and subtraction problems to assist with recall of the following strategies. If time allows, post another similar problem so students can relate previous strategy to new problem. Students show thumbs up when they have an answer in mind. The teacher checks with a few on their answer. Then he/she asks, “How did you solve this problem?” The teacher writes how each student solved the problem.

# Number Talks Part 1: Subitizing and Number Bonds KG-1st grade

A Number Talk is an opportunity to review number sense and operations by making it part of your daily math routine — so that what has previously been taught is not easily forgotten.

In this post I will expand on 2 methods for conducting a Number Talk session for KG-1st grade students (Subitizing and Number Bonds). Refer to a previous post (Sept. 10 – Daily Practice to Build Number Sense), in which I mentioned several other ways to review math concepts on a daily basis such as calendar topics, weather graphs, counting # of days of school, using a 100 chart, Choose 3 Ways, etc. Continue reading

Number Bonds are pairs of numbers that combine to total the target or focus number. When students learn number bonds they are applying the commutative, identity, and zero properties. PLUS, the information can be applied to both addition and subtraction problems. Number bonds of 10 are very critical to our place value system, and will enhance a student’s success with future addition and subtraction strategies such as use of an open number line.

• KG students should master number bonds to 5.
• First graders should master number bonds to 10.
• Second graders should master number bonds to 20.

# Using Color Tiles to Measure Area of Irregular Shapes

by C. Elkins

I have heard from a few 4th grade teachers that a new standard is difficult for their students to grasp. It is 4.GM.2.2: Find the area of polygons that can be decomposed into rectangles.

I have a couple of suggestions which help students with a concrete-pictorial-abstract progression approach to this problem (which is more developmentally appropriate).

1. I have attached an activity which involves the use of 1” color tiles to partition off irregular shapes and then determine the area of each smaller rectangle. It’s free and in 2 parts:
2. I located an excellent reference which shows pictorially how to do this step-by-step. It also includes good information about perimeter. It is:  Area and Perimeter

# Growing Patterns and Evaluating Expressions (1st – 5th grade)

For the teachers in OK, there have been many changes to the math standards, called OAS (Oklahoma Academic Standards). For 3rd, 4th, and 5th grades there is a stronger (or new) emphasis on growing patterns in the algebraic reasoning section. As I always advocate, connecting this concept to concrete objects and pictorial representations should happen before students are given a string of numbers and a function table to decipher.

Did you know there is more than one type of pattern? Continue reading

# Resources

See the menu bar above for a list of math and literacy resources. For now, I have listed some of my favorite websites which emphasize instructional strategies. Do you have favorites you would like to share? Click on the speech bubble and let us know!

# Daily Math Meeting Part 1: Ways to Build Number Sense K-5

To build number sense, students need frequent exposure or review of concepts you have previously introduced. There are many ways to build number sense on an on-going, informal basis – especially when you can squeeze in 10-15 minutes daily:

• During morning meeting time
• During a Number Talks session
• At the beginning of your math lesson
• At the end of your math lesson
• End of day closure time

I have included several of my power point slides on this topic as a PDF file (daily-practice-to-build-number-sense-pdf). Continue reading

# Subitizing – What does that mean?

by C. Elkins, OK Math and Reading Lady (updated post on 8-12-17)

The term “subitize” means to recognize quantity without counting. It is a concept recently added to the new OAS (Oklahoma Academic Standards). KG students should be able to “recognize without counting the quantity of a small group of objects in organized and random arrangements up to 10.” For first graders, the quantity is increased to 20 of “structured arrangements.” Subitizing is an important pre-requisite skill to learning addition and subtraction number combinations or number bonds.

Suggested items for the teacher to present this concept:

• Dot cards
• Ten frames and 2-color counters or tiles
• Dot dice
• Dominoes
• Tally marks