Multiplication: Building Arrays

Math AllianceMay 18, 2010

Melissa Hedges Beth Schefelker

Finding Easier Facts Inside Hard Facts

What Is your go-to strategy for helping students learn their multiplication facts?

What is your back-up strategy when the first one fails?

What is your Back-up to the Back-up?

What facts do you struggle with?

List 3-4 multiplication facts that you have a hard time remembering.

Think about how you find Your answer or how you remember it?

Share

“What Is a 3 by 4?”

What is an Array? An array is any arrangement of

things in rows and columns, such as a rectangle of square tiles or blocks.

Is there a difference? Rows Columns

Breaking Apart a 3 x 4 Array

What are the ways a 3 x 4 array can be broken apart?

(3x3) + (3x1) (3x2) + (3x2) (2x4) + (1x4)

Breaking Apart a 3 x 4 Array

What are the ways a 3 x 4 array can be broken apart?

(3x3) + (3x1) (3x2) + (3x2) (2x4) + (1x4)

Breaking Apart a Hard Fact

6 x 8 Pretend you don’t know the Answer to 6 x 8.

Partition the array into no more than 2 easier problems.

Cut apart and glue down the arrays you created.

Keep track of the way you partition them. Use numbers Use colors

Connections to Supporting Student Thinking

In what way would this strategy support students who are struggling with math facts?

How might knowing these facts help you solve 6 x 8?

2 x 8 6 x 4 4 x 8 6 x 3 5 x 8 6 x 5

Basic Facts for Upper-Grade Students

If students haven’t

Mastered multiplication facts by 5th or 6th grade need something other than more drill.

What Can Be done?

Recognize More Drill Work Won’t help.

Inventory the known and unknown Facts

Suggest Strategies

Diagnose strengths and weakness

Final Thoughts

• Students who have command of basic facts do not necessarily reason better than those who haven’t Mastered their facts yet.

• Mathematics is about reasoning, patterns and making sense of things.

• There is no reason why a child who has not mastered basic facts should be excluded from mathematical experiences.

Homework

Dot Images - Try the activity "Dot Images" numerous times.  Make sure to select images that are challenging and yet appropriate for your students.  Write up a brief description of the images you selected, why you selected them and what insights you gained about how your students ability to visualize multiplicatively.

Splitting Arrays - Complete the practice sheets "Splitting Arrays".  You will be using the practice sheets to split several arrays into helping facts and notate the equations that match each array. You will be asked to use the same arrays and find two different helping facts for each one.  In order to complete this homework, you will receive two copies of the practice sheet.  Follow the directions at the top as well as at the bottom of the sheet.