Lesson 39: Division Problems
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 39)
- 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. Show a division math fact (8÷4=2) and label each part of the equation. Then show the multiplication fact for this (2×4=8). You may choose to show a few other examples.
Step 2: Vocab Review (5 min)
Review prior vocabulary: division, divide, dividend, quotient, divisor, inverse operations, division symbol, and fact families. Introduce tally marks and how to make and group them. 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)
Now, with that same problem (8÷4=2), take 8 counters and divide into four groups, placing one counter in each group as you go, until all 8 are gone. Ask how many counters are in each group (2). Once you have modeled in the concrete, show how you can skip count by 4’s to get to 8 on the whiteboard (4, 8), and one way to do this is without forgetting how many you have skip counted is to place tally marks above the equation to keep track of your skip counting (would look like this: I I, indicating 2). Show a few other examples. Write a few word problems and dissect (e.g. 20 circles can be separated into __ groups of 10; 25 students can be separated into 5 groups of ___; 12 brownies can be separated into ___ groups of 4).
Step 4: Guided Practice (5 min)
Do the same activity from modeling, but now allowing students to work in pairs or groups. Give students an equation but this time, ask then to solve for the unknown quotient or unknown factor (divisor): 10÷2= ___, 15÷___= 5. Remind students to skip count by the factor given (for 10÷2, they can skip count by 2’s until they get to 10. To keep track of how many times they skip counted, they will need to make tally marks, or another visual: 2, 4, 6, 8, 10 would equal 5 tally marks, thus 10÷2=5). In the next problem, 15÷___= 5, remind students that they have the quotient, so they can go backwards and use multiplication to skip count until they get to 15, which will tell them their missing factor/divisor (3). Students may use TouchMath’s Foam Numerals to skip count, multiplication chart, skip counting songs, counters, or other resources. Try another 1-2 examples using working with manipulatives and then using tally marks while skip counting. If easier, students can place TouchPoints on the other numbers to skip count as well.
Step 5: Student Practice (5 min)
Go to Student Workbook Page (39). Read the directions at the top of the page. Tell students they will solving for the unknown quotients by drawing arrays, using TouchPoints to skip count, or skip count while using tally marks to solve. For the first two, show various ways they can solve, allowing students to choose for the rest. At the bottom of the page, have students fill in the correct answer with each word problem. Remind students to solve using whatever method they prefer – drawing arrays or other visuals, skip counting with tally marks, or using the 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.
