Close this search box.
TouchMath Extend

Lesson 36: Fact Families 1

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 36) 
  • 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)

Introduce the vocabulary presented within this 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 (5×4=20), using arrays as a visual. Then, show the division problem for this indicating this is part of the fact family for the multiplication shown (20÷4=5), illustrating that 20 is being equally separated into 4 groups (each group getting 5). Make real life connections with this (e.g. There are 20 students in our class, and I need to make 4 groups of equal students for our stations of games. There will be 5 students in each group of 4).  

Step 2: Vocab Review (5 min)

Review prior vocabulary: repeated addition, arrays, products of multiplication problems, and factors, and skip counting. Introduce new vocabulary: division, divide, dividend, quotient, divisor, inverse operations, division symbol, and fact families. Show a basic division problem and label each part (6÷2=3; 6 is the dividend, 2 the divisor, and 3 the quotient). Explain that the problem is asking how many sets of 2 you can make with 6. Things to know: the divident 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 3×2=6 and 6÷2=3). 

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).  

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 3 groups of dots and there are 2 dots in each group. Therefore, my multiplication sentence is 3x2=6. There are 6 total dots altogether. This means the product of 3+3 is 6”). Ask what the repeated addition statements would look like (e.g. 2+2+2 OR 3+3). 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 (6 total dots ÷ 2 dots in each group = 3 total groups of dots; 6 is the dividend, 2 the divisor, and 3 the quotient). 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (36). Read the directions at the top of the page. Tell students they will be practicing multiplication problems by skip counting, using arrays, and with repeated addition. Then, they will solve for the division problem listed (understanding it is part of the same fact family), using their answers from the multiplication problem to solve. For the first problem, students will circle each group of 8, then fill in the answers to the repeated addition (8+8+8+8=32). Students may use multiplication charts or calculators to assist with computation, as needed. Students will write 4 groups of 8 is 32, write the product to 4×8 as 32 and then solve the division problem 32÷8 (4) as the opposite of their multiplication problem, understanding how they work together. Repeat the same steps for the next two problems, using all available resources as needed, including counters, drawing visuals or arrays, multiplication charts, skip counting on the TouchPoints, 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.