Assessment Management

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1 Area Objectives To provide experiences with the concept of area, distinguishing between area and perimeter, and finding areas of rectangular figures by partitioning and counting squares. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Count square centimeters. [Number and Numeration Goal 1] Partition rectangles and count unit squares to find the areas. [Measurement and Reference Frames Goal 2] Make rectangles. [Geometry Goal 2] Key Activities Children discuss the concept of area. They compare area and perimeter, including units used for each measure. They identify rectangles with the same area but different perimeters. Ongoing Assessment: Informing Instruction See page 696. Key Vocabulary surface Materials Math Journal 2, pp. 222A and 222B Home Link 9 6 My Reference Book, pp. 68, 69, 69A, and 69B per group: 3 copies of Math Masters, p. 434 or 3 sheets of centimeter grid paper straightedge ruler half-sheet of paper checkerboard (optional) centimeter cubes (optional) Playing the Equivalent Fractions Game or Fraction Top-It Math Journal 2, pp. 198, 199, 203, and 204 Fraction Cards (2 sets cut from Math Journal 2, Activity Sheets 5 and 6) counters (optional) Children identify equivalent fractions and compare pairs of fractions. Math Boxes 9 7 Math Journal 2, p. 223 Children practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Operations and Computation Goal 4] Home Link 9 7 Math Masters, p. 283 Children practice and maintain skills through Home Link activities. READINESS Finding the Areas of Geoboard Rectangles geoboard rubber bands pennies or counters (optional) Children create rectangles on a geoboard and then find the areas of those rectangles. ENRICHMENT Finding the Perimeter Math Masters, p. 434 centimeter grid paper (optional) Children draw as many different rectangles and squares as possible that have a perimeter of 12 centimeters. EXTRA PRACTICE Finding the Areas of Block Letters Math Masters, p. 284 checkerboard (optional) Children find the areas of block letters by counting centimeter squares. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 142 Children add the term area to their Math Word Banks. Advance Preparation Draw a 2 ft 3 ft rectangle on posterboard or on the board prior to the beginning of the Lesson. Teacher s Reference Manual, Grades 1 3 pp. 158, Unit 9 Measurement

2 Getting Started Mental Math and Reflexes Pose problems like the following: Which fraction is greater? 6_ 10 or 3_ 10 6_ 10 1_ 2 or 3_ 4 3_ 4 1_ 2 or 5_ 8 5_ 8 Math Message A checkerboard has 8 rows of squares. There are 8 squares in each row. How many squares does the checkerboard have in all? 64 squares Write or draw a picture to show your strategy on a half-sheet of paper. Home Link 9 6 Follow-Up Ask volunteers to share their findings. Have children share strategies for one or two of the Practice problems. 1 Teaching the Lesson Math Message Follow-Up Ask children to share their solution strategies. Some possibilities: Make an 8-by-8 array; count by 8s; find 8 8 from memory, by using a facts table, or by using a calculator. Developing the Concept of Area (My Reference Book, pp. 69 and 69A) Begin an informal discussion about surfaces. To support English language learners, record the key ideas on the board. Ask: What is a surface? The top or outside of an object What are some examples of a surface? A tabletop, the floor, a checkerboard, the cover of a book, the top of a lake, and so on Most surfaces have boundaries, or borders. Boundaries give a surface its shape. Use the examples from the question above to help children understand boundaries. When we measure the amount of surface inside a shape, we are finding the area of the shape. As a class, read about area in My Reference Book, pages 69 and 69A. Remind children of the different ways in which they have tiled surfaces. (See Exploration E in Lesson 4-7.) They covered surfaces without gaps or overlaps using multiples of identical shapes. Point out that they were finding the areas of the surfaces. In Exploration B in Lesson 9-6, children measured area using a square grid. Area can be measured in square standard units, such as square inches (squares measuring 1 inch on each side), square feet, square centimeters, or square meters. ELL Links to the Future This is a beginning exposure to finding area. Children practice partitioning rectangles and counting square units to find the area. Partitioning rectangles and counting unit squares to find the area of rectangular shapes is a Grade 2 Goal. Describing and using strategies to estimate and calculate area is a Grade 4 Goal. Using a formula to calculate area is a Grade 5 Goal. Student Page Sometimes you want to know the amount of surface inside a shape. This amount of surface inside a shape is the area of the shape. Count the squares to find the area Each square is 1 square centimeter. The area of the shape is 15 square centimeters. Measurement Note Use square units for the area of a shape. Try It Together Draw a shape that has a perimeter of 10 inches. Compare your shape with a partner s shape. My Reference Book, p. 69 Lesson

3 Date 9 7 Teaching Master Finding Area Time For each shape, count the square centimeters to find the area Comparing Units Used to Measure Area and Perimeter (My Reference Book, p. 68) Area = sq cm Area = sq cm Use the tick marks to draw lines to show square units. Then count the squares to find the area in. 2 in cm Area = sq in. Area = sq cm 4 cm 6 12 Math Journal 2, p. 222A Refer back to the Math Message problem. Remind children that the checkerboard has 64 squares. Explain that the sides of each square on the checkerboard are 1 inch long. Each square is 1 square inch. The area of the checkerboard is 64 square inches. Read My Reference Book, page 68 to review perimeter. Ask: How would you find the perimeter of the checkerboard? Add the lengths of all the sides How long is each side of the checkerboard? 8 inches What is the perimeter of the checkerboard? 32 inches How did you find the perimeter? Sample answers: I added ; I multiplied 8 4. Call attention to the difference between the units for area and the units for perimeter. Because 32 is half of 64, does it make sense to say that the perimeter of the checkerboard is half its area? No; perimeter and area are measured using different units and cannot be compared in this way. How are the units for measuring area different from the units used for measuring perimeter? The units for perimeter measure the distance between points along a line segment; the units for area measure a surface. Rectangles with an area of 12 square centimeters Date 9 7 Time Finding Area continued For each shape, use the tick marks to draw lines to show square units. Then count the squares to find the area in. 3 in in. 1 cm 2 cm 3 cm Area = 5 sq in. Area = 15 sq cm Try This 7. Draw tick marks and line segments to make square units. Then count the squares to find the area. 6 cm 4 cm Area = 24 Student Page sq cm 3 cm 3 cm 6 cm Investigating Perimeter and Area (Math Masters, p. 434) SMALL-GROUP Distribute several copies of Math Masters, page 434 or sheets of centimeter grid paper to each group. Ask children to draw as many different rectangles as they can whose area is 12 square centimeters each. Ask them to find the perimeter of each rectangle. After children complete this task, bring the class together and go over the answers. There are three rectangles whose sides have whole-number lengths. (See margin.) Some children may suggest other rectangles, such as 1 1_ cm 8 cm. 2 Using Square Units to Find Area (My Reference Book, p. 69B) As a class, read My Reference Book, page 69B. Draw and label a 2 ft 3 ft rectangle on the board. First, draw tick marks at each 1 foot measure along the sides of the rectangle. Then, draw lines to connect the tick marks to make square feet. See below. 3 ft 3 ft Math Journal 2, p. 222B 2 ft 2 ft 696 Unit 9 Measurement

4 Ask children to count the squares inside the rectangle. 6 Remind children that since all the sides of the squares measure 1 foot, the area of the rectangle is 6 square feet. Write area = 6 square feet under the rectangle. Ask children why the example in My Reference Book is square centimeters. Because each side of each square is 1 centimeter Counting and Drawing Square Units to Find Area (Math Journal 2, pp. 222A and 222B) Children complete journal pages 222A and 222B. When children are partitioning shapes it is not necessary for them to use a ruler or straightedge. 2 Ongoing Learning & Practice Playing the Equivalent Fractions Game or Fraction Top-It (Math Journal 2, pp. 198, 199, 203, and 204) PARTNER Date 9 7 Math Boxes 1. Draw two ways to show 2_ 3. Sample answers: 3. Get 36 counters. Share them equally among 4 children. How many counters does each child get? 9 counters How many are left over? 0 5. Solve. counters = = = = Student Page Unit Time Math Journal 2, p Write 3 even numbers larger than 100. Sample answers: 102, 110, 200 Write 3 odd numbers smaller than 100. Sample answers: 5, 23, I have $2.00. Can I buy 4 bags of chips for $0.55 each? no 6. In 43,692, the value of 4 is 40, is 3, is is is Children use Fraction Cards to identify equivalent fractions and compare pairs of fractions. See Lessons 8-5 and 8-6. Math Boxes 9 7 (Math Journal 2, p. 223) Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 9-5 and 9-9. The skill in Problem 6 previews Unit 10 content. Writing/Reasoning Have children draw, write, or verbalize their answer to the following: Explain your answer to Problem 4. Sample answer: $0.50 times 4 is $2. $0.55 is more than $0.50, so 4 bags of chips will cost more than $2. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 3 Use Math Boxes, Problem 3 to assess children s understanding of equal shares. Children are making adequate progress if they are able to complete the box accurately using counters or drawings. [Operations and Computation Goal 4] Name Date Time HOME LINK 9 7 Area and Perimeter Family Today children discussed the concept of finding the area of a surface. Area is measured by Note finding the number of square units needed to cover the surface inside a shape. Make sure your child understands that, when he or she is finding the perimeter of the letters in Problem 4, he or she is finding the distance around the outside of the letters. 69 Please return this Home Link to school tomorrow. Find the area of each letter Home Link Master 11 Area = sq cm Area = sq cm Area = sq cm 4. What is the perimeter of each letter? I: cm U: cm J: cm Home Link 9 7 (Math Masters, p. 283) 5. Use a straightedge and the tick marks to draw square units. Count the squares to find the area. Area = 12 sq cm Home Connection Children find the areas and perimeters of letters. Practice = = Math Masters, p Lesson

5 Name Date Time 9 7 Letter Areas Find the area of each letter Area = sq cm Area = sq cm Area = sq cm 4. Teaching Master 5. Area = 7 sq cm Area = 11 sq cm Area = 7 sq cm Differentiation Options READINESS Finding the Areas of Geoboard Rectangles To explore the concept of area as measuring a surface with square units, have children make rectangles on a geoboard and count the squares to find the area. Children can place a penny or counter in each of the square units. (See margin.) Try This An 8-by-8 checkerboard has 64 squares. Some squares on a checkerboard are white. Some are black. Squares of the same color are never next to each other. 7. How many white squares 8. If the square in one corner is are in each row? 4 black, what color is the square How many black squares? 4 in the diagonal corner? black ENRICHMENT Finding the Perimeter (Math Masters, p. 434) Math Masters, p. 284 To apply children s knowledge of perimeter, have them draw on grid paper as many different rectangles and squares as they can that have a perimeter of 12 centimeters (rather than an area of 12 square centimeters). When they have finished, ask children to describe how they know they have found all the rectangles. Encourage them to use vocabulary from this unit. Discuss whether the areas are the same in all the shapes. Discuss which shape has the largest area. Finding the area of a geoboard rectangle with 5 rows and 4 columns EXTRA PRACTICE Finding the Areas of Block Letters (Math Masters, p. 284) Children find the areas of block letters. Have children work on the Try This problems at the bottom of the page. You might want to display a checkerboard or model one on the board. Planning Ahead To do the demonstration in Lesson 9-8, you will need labeled containers, such as milk cartons and beverage bottles, with these capacities: half-pint, pint, quart, half-gallon, gallon, and liter. Write the capacity on each container or circle the capacity if it is printed on the container. Use a colored marker or a hole in the container to show the fill level of each container. You will also need a funnel, a tray, and at least 1 gallon of a pourable substance, such as water, sand, or rice. In Lesson 9-9, children will weigh pennies on a spring scale. Attach a paper or plastic cup to the spring scale to hold the pennies. Each group will need about 40 pennies in a container. ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. 142) SMALL-GROUP To provide language support for measurement, have children use the Word Bank template found on Differentiation Handbook, page 142. Ask children to write the term area, draw a picture representing the term, and write other related words. See the Differentiation Handbook for more information. 698 Unit 9 Measurement

6 Name Date Time HOME LINK 9 7 Area and Perimeter Family Note Today children discussed the concept of finding the area of a surface. Area is measured by finding the number of square units needed to cover the surface inside a shape. Make sure your child understands that, when he or she is finding the perimeter of the letters in Problem 4, he or she is finding the distance around the outside of the letters. Please return this Home Link to school tomorrow. 69 Find the area of each letter Area = sq cm Area = sq cm Area = sq cm 4. What is the perimeter of each letter? I: cm U: cm J: cm Copyright Wright Group/McGraw-Hill 5. Use a straightedge and the tick marks to draw square units. Count the squares to find the area. Area = sq cm Practice = = 283

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