Lesson 38: Division with Visual Support
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
Materials
- Extend Workbook (Page 38)
- 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 4×3=12 and 12÷3=4).
Step 3: Model (5 min)
For this lesson, start off by showing the dividend with counters (e.g. 12) and count the total. Ask students how many total counters there are (12), then separate into three groups. Ask the students how many groups there are (3), and then how many counters are in each group (4). See if any student can determine the division equation 12÷3=4. Review the parts of a division equation (dividend, divisor, and quotient). Put the 12 counters back together, and now ask them how they can reverse the factors to stay in the same fact family (12 counters, split into 4 groups, with 3 counters in each group: 12÷4=3). 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 5’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 4 groups of dots and there are 5 dots in each group. Therefore, my multiplication sentence is 4x5=20. There are 20 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 (20 total dots ÷ 5 dots in each group = 4 total groups of dots; 20 is the dividend, 5 the divisor, and 4 the quotient). Ask students to find the other fact family in this group (20÷4=5). Try another 1-2 examples of easier fact families.
Step 5: Student Practice (5 min)
Go to Student Workbook Page (38). Read the directions at the top of the page. Tell students they will be focusing on fact families, and this time they will be given the dividend (total number of dots that will need to be circled to show the equal number of groups being divided). From here, they will need to indicate how many dots are within each group, and then determine what is the correct division equation (two are incorrect). 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.
