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Patterns of Multiplication Facts within 100

Key Concepts

We can multiply within 100 using different methods
Multiplication chart
Pattern in multiplication table.
Distributive property of multiplication
Identity Property
Zero Property

Introduction 

1.1 What is Multiplication Chart

  • A multiplication chart is a table that shows the product of two numbers 
  • Usually, one set of numbers is written on the left column and another set is written as the top row. The products are listed as a rectangular array of numbers. 
  • A multiplication table helps us to see lots of products at the same time. 
  • For example, a multiplication chart of 10 can be written as: 

Multiplication is repeated addition 

There are 3 groups of 4 lollipops each. That is, the total number of lollipops is 3 times 4  or  4+4+4  or 12. 

A simple way to the day-to-day calculations is through the help of a multiplication chart. 

  • Step 1: Choose the first number from the numbers listed in the left-most column and the second number from the top-most row. 
  • Step 2: Starting from the first number move towards the right and starting from the second number move towards down.  The square where the two numbers meet gives the product. 
  • For example   5 × 4 
Multiplication Example

1.2 Patterns in Multiplication 

Properties can be used to understand a pattern. 

For example 4×6 is double of 2×6 

Solution: 

2×6=12 

4×6=12+12 

4×6=24 

Because 4 is the double of 2, the product of any number multiplied by 4 will be double the product of that same number multiplied by 2. 

  • We can shade the columns for 0,2,4,6,8 and 10. 
  • We can see that all the products in these columns end in 0,2,4,6,8. 
  • All the products are even numbers. 
  • All the products of 4 are double the products of 2 
  • All the products of 6 are double the products of 3 
  • This works for products of 8 and 4, and it works for products of 10 and 5 as well. 

1.3 Distributive Property: 

  • If we look at the columns 2,4, and 6, we see the products for 6 are the sum of the products for 2 and 4. 
  • 2+4=6 
  • This pattern happened because the Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number , then adding the products. 
Distributive Property

This works for the columns for 2,4,and 6 because  

2+4=6 

 

For Example: 

3×6 = 3× (2+4) 

         = (3×2) +(3×4) 

         = 6+12 

         = 18 

It will also work for the columns 

1,2, and 3             1+2=3 

1,3, and 4             1+3=4 

And many others. 

Example: 

One toy dog uses 4 batteries. How many batteries are needed for 6 toy dogs? 

we can describe a pattern in a table. 

Dog

We look for the pattern to complete the table. We can look across the rows to see that the number of batteries increases by 4 for each toy dog. 

By comparing columns in the table, we can multiply the number of toy dogs by 4 to find the number of batteries that are needed. 

For 6 toy dogs we need, 6×4 =24 batteries 

1.4 Distributive Property: 

The identity property of multiplication states that if you multiply any number by 1, the answer will always be the same number. 

Example: 

5 × 1 = 5 

11 × 1 = 11 

1.5 Zero Property: 

Diagram

Description automatically generated

The Zero Property of multiplication states that when we multiply a number by zero, the product is always zero. 

Example

7 × 0 = 0 

25 × 0 = 0 

1.6 Fact Family 

A fact family can be defined as a group of math facts or equations created using the same set of numbers. The fact family shows the relationships between the three numbers involved. 

Shape

Description automatically generatedExample: 

6 × 7 = 42 

7 × 6 = 42 

42÷7 = 6 

42÷6 = 7 

Example: 

Tanya buys 9 pack of bananas. Each banana packet has 5 bananas. How many bananas did Tanya buy in all? 

Solution

Number of banana packets = 9 

Number of bananas in each packet = 5 

Total number of bananas = 9 × 5 

= 45 

Table

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What we have learnt :

A multiplication chart is a table that shows the product of two numbers
A multiplication table helps us to see lots of products at the same time.
All the products of 4 are double the products of 2
Distributive Property is: a ×(b + c) = (a × b) + (a × c)
Identity property states that any number is multiplied by 1, the answer will be same number.
Zero property states that any number is multiplied by zero, the answer will be zero.
A fact family is a group of calculations that are created using the same three numbers.

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