Multiplication and Area
Students will be able to find the area of a rectangle using addition and multiplication in the context of real-world problems.
- Hold up a piece of white 8x10 paper. Ask students, "How can we measure the entire surface of this paper?"
- Demonstrate what the area is using paint as a visual and explain, "You may know how to measure lines, like the sides of this piece of paper (paint a thin line along each side of the paper), but when we measure the space inside a shape, we need to use a special formula. This is called the area (paint the entire surface of the paper) and today, we are going to learn how to measure it using square units."
- Hang the painted paper on the board to revisit later.
Explicit Instruction/Teacher modeling(15 minutes)
- Display graph paper and shade in one unit. Explain that this is one square unit.
- Tell students, "We can measure the area of a square or rectangle using square units."
- On the graph paper, draw a rectangle that is 2x3 units and shade or highlight the inside of the shape.
- Reiterate that the area is the inside of the shape and explain that we can determine the area by counting how many square units fit inside the shape. Count the units aloud (6 square units) and write 'Area = 6 square units’.
- Draw a second rectangle that is 4x7 units.
- Explain, "Counting units is one way to find the area, but it can take a long time when we have a larger rectangle like this one. We can use addition to help us find the area without counting all of the units."
- Circle each of the rows of seven and explain: we have four rows of seven units, so instead of counting all the units inside, I can add 7 + 7 + 7 + 7 to find the area. Write the addition problem and ask a student to solve. Write ‘Area = 28 square units’.
- Ask, "Is there another way I could find the area that is is faster than counting or adding the units?"
- Have students talk to a partner. Ask for volunteers to share their ideas. Then discuss, "We can multiply to find area. Do you see that 7 + 7 + 7 + 7 is the same as 4 x 7?
- Write ‘4 x 7 = 28 square units’.
- Handout the area worksheet and review the top section that gives the formula for area (Area = Length x Width).
Guided Practice(5 minutes)
- Have students work with a partner to complete the “try it” problem on the worksheet.
- Review the problem as a class.
Independent working time(15 minutes)
- Have students complete problems 1 to 4 on the worksheet independently.
- Circulate and offer support as needed.
- Review the worksheet as a class.
- Have students to count square units to find the area or to check their work.
- Have students use repeated addition to find the area.
- Provide one or both dimensions and ask students to multiply using a multiplication table as a scaffold.
- Have students complete the challenge portion of each problem on the worksheet.
- Hold up or display a rectangular shape cut from grid paper. Ask students to explain how they would find the area of the shape. Take note of students who count units to find the area and reteach the algorithm as needed.
- Use the “more practice” portion of the worksheet as an additional assessment. Hand out the page and have students complete the two problems independently.
- Collect and check for understanding.
Review and closing(7 minutes)
- Direct students’ attention to the painted 8x10 paper on the board. Point out that the paper does not have any square units printed on it.
- Ask, "How can we determine the area of this paper?"
- Give students time to talk with a partner, then discuss as a class (i.e. we can measure the length and width of the paper and multiply to find the area).
- Invite a student to measure the length and width of the paper. Then, write ‘Area = 8 inches x 10 inches’ on the board. Ask students to solve for the area.
- Explain, "Since we measured the length and width in inches, the area will be expressed as square inches instead of square units. Add ‘square inches’ to the answer (80 square inches)."