Introduction to Division with Remainders
Students will be able to divide whole numbers with remainders using base ten blocks and standard algorithm.
- Using a projector, demonstrate how to divide with a remainder by building the solution to a problem with base ten cubes (e.g., 14 ÷ 4).
- Point out the remainder in your solution, and define the term (e.g., "After dividing a number into equal groups, the remainder is the whole number that is left over, or remaining.").
Explicit Instruction/Teacher modeling(10 minutes)
- Build another problem with base ten blocks (e.g., 35 ÷ 2).
- Draw the same problem in a math notebook, using a projector to show students the process.
- Teach the standard algorithm for the same example and discuss how the algorithm is connected to the visual representation.
- Repeat with another example like 134 ÷ 3 (build, draw, algorithm).
Guided Practice(15 minutes)
- Hand out base ten blocks so that every student has a set.
- Write a problem on the board and have students build it with a partner. Then have them draw their solution in their own math notebook (e.g., 17 ÷ 5).
- Invite a volunteer to show their drawn solution to class.
- As a class, solve the same problem with the standard algorithm.
- Repeat with another example, like 53 ÷ 3 (build, draw, algorithm). But this time, have students use the algorithm with their partner. Then, review as a class.
Independent working time(20 minutes)
- Give each student a strip of three problems so that students seated near one another have different strips. Ensure that before copying & cutting the worksheet into strips, you have labeled each row (A, B, C).
- Instruct students to build the first problem listed on their strip with blocks, draw the second, and solve the third with the standard algorithm.
- Circulate the room as students work and provide support as needed.
- Organize a jigsaw review:
- Group students according to which strip of problems they solved and have them review their process and solutions as a group (e.g., students with the strip labeled "A" would check their work with other "A's"). Note: students may need to rebuild their solution to problem one as a group in order to check their work.
- Check in with each group as they review. (Optional: take photos of their base ten block solutions to display or add to math notebooks.)
- Give students the same strip of problems as their seat partner so they can work together to solve them.
- Provide a pre-drawn solution and have students build it using blocks.
- Group students into smaller groups during the jigsaw review so that only 3–4 students are in each group. (Note: in this scenario, you will have more than one group reviewing each strip of problems.)
- Have students write a word problem using one of the problems on their strips.
- Have students solve word problems with remainders (see optional materials for a sample worksheet).
- On a half sheet of paper, assign students from each jigsaw group a division problem (e.g., "If you were in group A, solve 18 ÷ 5"). This will ensure that students are solving a different problem than their seat partner, so that the assessment is completed independently.
- Have them write their problem at the top of their scratch paper, then instruct them to draw the problem on one half of the paper and solve it with the standard algorithm on the other. Collect and check for understanding.
Review and closing(5 minutes)
- Display a division problem, using the standard algorithm, which is solved incorrectly (e.g., 62 ÷ 5 = 11 r7).
- Have students correct the problem by drawing it out and ask them to explain what was wrong with the other solution (e.g., "The remainder shouldn't be greater than the divisor.").
- Ask students to consider the role of remainders and discuss. (i.e., What happens to remainders after we solve a problem? Are remainders important? When might we use division and need to consider the remainder?)