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TouchMath Extend

Lesson 40: Fact Families 3

Lesson Objectives

  • Extend learning of the relationship of multiplication and division. 
  • Use objects, pictures, drawings, and number lines to understand multiplication and division 
  • See division as finding unknown factors in multiplication 
  • Use patterns to find quotients 
  • Apply skip counting and the TouchMath approach for finding products and quotients 
  • Apply understanding of division as an inverse operation of multiplication 


  • Extend Workbook (Page 40) 
  • 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 (7x5=35), using arrays as a visual. Then, show the division problem for this indicating this is part of the fact family for the multiplication shown (35÷5=7), illustrating that 35 is being equally separated into 5 groups (each group getting 7).   

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 (30÷5=6; 30 is the dividend, 5 the divisor, and 6 the quotient). Explain that the problem is asking how many sets of 5 you can make with 30. 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 5×6=30 and 30÷5=6). 

Step 3: Model (5 min)

For this lesson, start off by showing the dividend with counters (e.g. in this example, 20) and count the total. Ask students how many total counters there are (20), then separate into 4 groups. Ask the students how many groups there are (4), and then how many counters are in each group (5). See if any student can determine the division equation 20÷4=5. Review the parts of a division equation (dividend, divisor, and quotient). Put the 20 counters back together, and now ask them how they can reverse the factors to stay in the same fact family (20 counters, split into 5 groups, with 4 counters in each group: 20÷5=4). Then, review teaching how to skip count by one number while touching the TouchPoints on the other number, using TouchMath’s Foam Numerals. Show another division problem using counters or on the white board, and model breaking into equal parts and labeling each part. 

Step 4: Guided Practice (5 min)

Do the same activity from modeling, but now show a few different division equations and ask students which is the correct equation. Then, in groups, ask students to draw arrays with dots or use physical counters with multiples of 6’s for review, using a multiplication chart as support. 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 5 groups of dots and there are 6 dots in each group. Therefore, my multiplication sentence is 5x6=30. There are 30 total dots altogether. Ask what the repeated addition statements would look like and then have students practice skip counting by one number while touching the TouchPoints on the other number using TouchMath’s Foam Numerals. Next, have students create the division equations within that fact family, labeling the parts with support (30 total dots ÷ 6 total groups of dots = 5 dots in each group; 30 is the dividend, 6 the divisor, and 5 the quotient). Ask students to find the other fact family in this group (30÷5=6). Try another 1-2 examples of easier fact families. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (40). Read the directions at the top of the page. Tell students they will be focusing on fact families and finding unknowns in the four total equations for the set multiplication/division fact families. One equation will be fully given to them, and they will use the information in that first equation to identify the unknown factors, products, or quotients in the other equations within that fact family.  

In the first set of equations, 6×4=24 is given. Ask students how they could rewrite that multiplication problem, ending in the same product (4×6=24). Then, ask them to focus on the inverse operations of that fact family (24÷6=___ and 24÷___=6). In this case, students can recall from their guided activities that factors will be reversed and 24÷6=4, and 24÷4=6. If they are struggling with this concept, remind them that they can use their TouchMath Foam Numerals, they can create arrays using the information they have to group or break apart numbers, they can use counters or manipulatives, or they can skip count the TouchPoints on the other factor to either multiply or divide (using tallies). Repeat these steps for the next five sets of fact families. 

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.