Finding Fair Shares

Our class is starting a new math unit about fractions called Finding Fair Shares. In this unit, students investigate the meaning of fractions and the ways fractions can be represented. Students will solve sharing problems (How can 2 people share 3 brownies equally?), building wholes from fractional parts (1/2+ 1/4 + 1/4= 1), and find fraction equivalents (2/3 = 1/6). The kitchen is an excellent place to give your child hands-on experience with fractions.

We are so excited to share with you the closing meeting from our very first fraction lesson this year. Check out the great thinking below!

Fraction Fun from Melissa Ross on Vimeo.

Literature Connection: Here are some suggestions of children's books that contain relevant math ideas about fractions. Look for these books at your local library:

The Doorbell Rang by: Pat Hutchins
Fraction Action by: Loreen Leedy
Eating Fractions by: Bruce McMillan

Multiplication and Division Strategies

Below is a video clip from our math closing meeting yesterday. Check out these great strategies for multiplication and division!

Multiplication and Division Strategies from Melissa Ross on Vimeo.

Arrays Make Math Easy to Visualize

This week in math, we are exploring the use of arrays to help us with multiplication and division. It is imperative that students develop strong visual images of multiplication as they develop strategies for solving multiplication problems. If a student can clearly visualize how the numbers they are multiplying are related, they can develop flexible, efficient, and accurate strategies for solving multiplication problems. One way for students to visualize these relationships is through the use of arrays. An array is an arrangement of an equal number of items in rows and columns. Arrays can helpful when solving more “difficult” multiplication situations. Being able to visualize how to break multiplication problems into parts becomes even more important as students solve multi-digit problems in Grades 4 and 5.

The following is an example of how a student can split an array into smaller arrays making it easier to find the product. (In case you have forgotten, a product is the answer to a multiplication problem.)

Another way students can help lay a strong foundation for multiplication is to practice skip counting by multiples of numbers 2-12. The goal is for students to be able to skip count fluently (within 3 seconds) from one multiple to the next.This task can be practiced at home, between commercial breaks, or even in the car. Being able to skip count fluently will undoubtedly help students in their work with multiplication and division. Check out this website that helps with skip counting.

Thank you to our guest author this week, Miss Russell. :)

Comparing Arrays

Last week in Math Workshop, we spent time arranging different amounts of chairs into rows and columns (arrays). Today, we are comparing the arrangement 16 and 17 chairs. Look at the different arrangements that we can make with each number below:

What do you notice about these arrays? Do any of the arrays have a special or unique shape? What do you notice about the number of arrays that can be made with 16 chairs compared to 17 chairs?

Hopefully, you notice that 16 chairs can be arranged in several different arrays. That is because it has many factors: 1, 2, 4, 8, 16. A number that has more than two factors is called a composite number. You probably noticed that 17 only has two arrays. This is because 17 is a prime number. Any number that has only two factors, one and itself, is a prime number. The factors of 17 are 17 and 1.

Also, you may have noticed that 16 can be arranged into a perfect square with 4 rows and 4 columns. Any number that results when another number is multiplied by itself is a square number. (ex: 3x3=9 Nine is a square number. 5x5=25 Twenty-five is a square number.) Sometimes math vocabulary can be confusing! For a reminder of the meaning of some math words that you may have forgotten, visit this great online math dictionary.

Thank you to our guest author this week, Miss Russell. :)

How Many Groups of 10?

There are 132 flyers that need to be handed out to Extended Day classes. The flyers need to be organized in stacks of ten to make them easier to hand out. How many stacks of ten will there be? How many flyers will be left over?

When looking at a two digit number, it is easy for students to determine how many tens and ones are in the number. When working with a three-digit number, students have to understand a little more about place value. In working with 100, students first need to understand how many tens are in each group of 100 in order to solve. This can be a little abstract for students at first.

To help them understand how many groups of 10 are in 100, we bring out the place value blocks for a visual. Let's start by representing the number 132 with place value blocks.

It is important for students to understand how many groups of 10 are in 100. By using the place value blocks, students can count the groups of ten easily.

When students understand that 1 group of 100 is equal to 10 groups of 10, they are able to solve these problems easily. Student work may look something like the following:

In the strategy above, the student drew a representation of the place value block model to explain her thinking.

In the strategy above, the student used a modified open number line to keep track of the number of groups of tens and singles.

In the final sample above, the student wrote what she knew about the number of groups of ten in 132. These are just several student samples. There are many more ways students can solve and model their thinking for problems like these.