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TouchMath Extend

Lesson 37: Fact Families 2

Lesson Objectives

  • Use objects, pictures, drawings, and number lines to understand multiplication and division 
  • See multiplication as repeated addition 
  • See division as finding unknown factors in multiplication 
  • Use patterns to find quotients 
  • Write equations of repeated addition and multiplication 
  • Apply skip counting and the TouchMath approach for finding products and quotients 
  • Apply vocabulary (factors and products) in explaining multiplication and division 
  • Apply understanding of division as an inverse operation of multiplication 


  • Extend Workbook (Page 37) 
  • Counters or manipulatives 
  • Highlighters, markers, or crayons 
  • TouchMath’s Foam Numerals and TouchPoints (for more concrete) 
  • Skip counting multiplication songs (multiples of 5) (as needed) 

Step 1: Warm Up (5 min)

Review the vocabulary from prior lesson. Write dividend, divisor, and quotient on the whiteboard. Explain that they will learn how to divide and that division is related to multiplication, just as subtraction is related to addition, and that they will use skip counting to find the answers, or answers to their multiplication problems to solve the division problems. Start off with a simple multiplication problem on the white board (2×8=16), using arrays as a visual. Then, show the division problem for this indicating this is part of the fact family for the multiplication shown (16÷8=2), illustrating that 16 is being equally separated into 8 groups (each group getting 2).   

Step 2: Vocab Review (5 min)

Review prior vocabulary: division, divide, dividend, quotient, divisor, inverse operations, division symbol, and fact families. Show a basic division problem and label each part (12÷3=4; 12 is the dividend, 3 the divisor, and 4 the quotient). Explain that the problem is asking how many sets of 3 you can make with 12. Things to know: the dividend is the largest number in a division problem, the divisor is the number that is used to divide – the number doing the dividing (the number of items in each group that we are separating, or dividing, the total into). Division is sharing equally with all members of a group. Fact families are a group of multiplication and division equations that use the same three numbers (e.g 4x3=12 and 12÷3=4). 

Step 3: Model (5 min)

Ask students to tell you how many counters are in each group (5) and then ask how many groups are there total (2). Tell students that this is the same thing as 5+5, which equals 10 total counters. Show several examples skip counting using counters or manipulatives, skip counting forward and backwards. Illustrate with arrays on the white boards and physical counters. Then, review teaching how to skip count by one number while touching the TouchPoints on the other number, using TouchMath’s Foam Numerals. Following this, model the inverse operation (division) and show how they are connected (modeling 10÷2=5 with arrays, physical counters, and TouchMath’s Foam Numerals). Expand on this and explain that 2×5=10 AND 5×2=10, so with 10÷2=5, you can reverse the factors, but will have a different quotient (e.g. 10÷5=2). However, both division equations are part of the same fact family as 2×5=10; the rest being: 5×2=10, 10÷2=5 and 10÷5=2). 

Step 4: Guided Practice (5 min)

In groups, ask students to draw arrays with dots/circles/dots with multiples of 2’s for review. Have students circle each group. Ask them, “how many groups of dots/stars did you circle? How many dots/stars are in each group?” Then have them write down their multiplication sentences/problems next to their arrays (e.g. “We circled 6 groups of dots and there are 2 dots in each group. Therefore, my multiplication sentence is 6x2=12. There are 12 total dots altogether. This means the sum of 2+2+2+2+2+2 is 12, and the product of 6×2 is 12”). Ask what the repeated addition statements would look like (e.g. 2+2+2+2+2+2 or 6+6). Have students practice skip counting by one number while touching the TouchPoints on the other number using TouchMath’s Foam Numerals. Then, have students show the division steps, labeling the parts with support (12 total dots ÷ 2 dots in each group = 6 total groups of dots; 12 is the dividend, 2 the divisor, and 6 the quotient). Ask students to find the other fact family in this group (12÷6=2). Try another 1-2 examples of easier fact families. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (37). Read the directions at the top of the page. Tell students they will be focusing on fact families, and after given a multiplication equation, will need to find the two division equations in that fact family. For the first problem, students will circle the two groups of 3 dots to show 3×2=6. Then they will solve for the two division equations, remembering that the largest number is always the dividend (6), and for the last equation, reversing the factors (instead of 6÷3=2, the second equation would be 6÷2=3). Repeat the same steps for the next three problems, using all available resources as needed, including counters, drawing visuals or arrays, multiplication charts, skip counting on the TouchPoints, and TouchMath’s Foam Numerals. 

Step 6: Wrap Up (5 min)

To wrap up the lesson, review the learning objectives and core vocabulary words again and ask your students about their experience.