How to Teach the Multiplication of Signed Numbers
Teach the basic rule., Review the rule pictorially as an array., Review the rule conceptually as repeated addition., Review practice problems.
Step-by-Step Guide
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Step 1: Teach the basic rule.
The rule is that a positive times a positive equals a positive.This is the basic way of multiplying that students first learn.
Remind students that numbers without a sign are assumed to be positive.
For example, 2×4=8{\displaystyle 2\times 4=8}. -
Step 2: Review the rule pictorially as an array.
This is what students do to conceptualize multiplication when they are first learning it in elementary school.
An array is an arrangement of shapes or objects in columns and rows.
The rows equal the number of groups you have, the columns equal how many objects in each group.
For example, to show 2×4=8{\displaystyle 2\times 4=8}, you would show an array of 2 rows and 4 columns.
Also show the problem applying the commutative property.
So, illustrate 4×2=8{\displaystyle 4\times 2=8} by drawing an array that shows 4 rows of 2 columns.
You an also use manipulatives or drawings to help students conceptualize that multiplication is a way to counted repeated, equal groups of objects.
For example, you can use 8 coins and arrange them into two groups of 4 to show that 4×2=8{\displaystyle 4\times 2=8}, or arrange the 8 coins into four groups of 2 to show that 2×4=8{\displaystyle 2\times 4=8}.
Use number stories to engage learners, such as "Nikki has two baskets.
She puts 4 apples in each basket.
How many apples does she have?"
You can use the arrays to show that when we multiply, we are simply adding groups of the same amount together.
One factor tells us the number we are adding, and the other factor tells us how many times we add it.For example, 2×4=2+2+2+2=8{\displaystyle 2\times 4=2+2+2+2=8}. , Give the student a number of multiplication problems.
Even if the student has the particular fact memorized, have him or her show how the multiplication problem represents repeated addition.
This will help them conceptualize multiplying with negative numbers. -
Step 3: Review the rule conceptually as repeated addition.
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Step 4: Review practice problems.
Detailed Guide
The rule is that a positive times a positive equals a positive.This is the basic way of multiplying that students first learn.
Remind students that numbers without a sign are assumed to be positive.
For example, 2×4=8{\displaystyle 2\times 4=8}.
This is what students do to conceptualize multiplication when they are first learning it in elementary school.
An array is an arrangement of shapes or objects in columns and rows.
The rows equal the number of groups you have, the columns equal how many objects in each group.
For example, to show 2×4=8{\displaystyle 2\times 4=8}, you would show an array of 2 rows and 4 columns.
Also show the problem applying the commutative property.
So, illustrate 4×2=8{\displaystyle 4\times 2=8} by drawing an array that shows 4 rows of 2 columns.
You an also use manipulatives or drawings to help students conceptualize that multiplication is a way to counted repeated, equal groups of objects.
For example, you can use 8 coins and arrange them into two groups of 4 to show that 4×2=8{\displaystyle 4\times 2=8}, or arrange the 8 coins into four groups of 2 to show that 2×4=8{\displaystyle 2\times 4=8}.
Use number stories to engage learners, such as "Nikki has two baskets.
She puts 4 apples in each basket.
How many apples does she have?"
You can use the arrays to show that when we multiply, we are simply adding groups of the same amount together.
One factor tells us the number we are adding, and the other factor tells us how many times we add it.For example, 2×4=2+2+2+2=8{\displaystyle 2\times 4=2+2+2+2=8}. , Give the student a number of multiplication problems.
Even if the student has the particular fact memorized, have him or her show how the multiplication problem represents repeated addition.
This will help them conceptualize multiplying with negative numbers.
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Peter Rivera
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