PUZZLES. Getting Ready. The Activity. Overview. Introducing

Transcription

1 PUZZLES Getting Ready What Yo ll Need Snap Cbes, 30 per pair Pzzle Shapes, pages Constrction paper, 14 sheets Snap Cbe grid paper, page 93 Overhead Snap Cbes and/or Snap Cbe grid paper transparency (optional) Overview Children estimate, then find the nmber of Snap Cbes reqired to cover the areas of figres. In this activity, children have the opportnity to: find the area of a variety of shapes discover that different shapes may have the same area develop estimation skills MEASUREMENT NUMBER GEOMETRY develop and se systems for conting grops of nmbers Conting Estimation Area Comparing The Activity After copying the five Pzzle Shapes pages, ct the 14 pzzle shapes ot and mont each one on constrction paper for children to se in On Their Own. Yo may need to point ot that, as children cover the pzzle shapes, they shold ignore the connectors on the ends of the Snap Cbes that lie beyond the otlines of the shapes. Introdcing Show children one of the Pzzle Shapes worksheets. Ask them for estimates of how many Snap Cbes will cover the shape. Place cbes on the shape. With the help of the class, cont the nmber of Snap Cbes needed to cover the shape. Explain that the word area is sed to describe the nmber of Snap Cbes needed to cover the shape and that the area of this figre is eqal to Snap Cbes. ETA hand2mind

2 On Their Own How many pzzle shapes can yo find that have the same area? Work with a partner and take 1 of the pzzle shapes from the classroom set. Estimate how many Snap Cbes wold completely cover the shape. Then place Snap Cbes on the shape to find the area. The area of the shape is the nmber of Snap Cbes that will exactly cover the shape. For example, this shape has an area of 12 Snap Cbes. Area = 12 Snap Cbes Compare yor estimate to the actal area of the pzzle shape. Record yor reslts by copying the pictre yo see on the shape. Write the area of the shape next to the pictre. Retrn the pzzle shape to the classroom set. Choose another shape that yo think has the same area as yor first shape. Find and record the area of this shape. Contine to choose shapes and find their areas. Check yor reslts to see if any of the shapes have the same area. Keep looking ntil yo find at least 1 pair of shapes with the same area. Look for shortcts for finding area. The Bigger Pictre Thinking and Sharing Write children s findings on the board. Yo might se sentences like this: Each of shapes and shape x have an area of 23 Snap Cbes. Use prompts sch as these to promote class discssion: How did yo find the area of these shapes? How close were yor estimates to the actal areas? (Point to one figre.) How wold yo estimate the area of this figre? How cold yo tell which pzzle shape has the greatest area withot sing cbes? What ideas do yo have for conting the cbes? Yo may want to post the pzzle shapes for reference. Writing Have children se Snap Cbes to create two different shapes that wold each cover an area of 15 Snap Cbes. Then have them trace the figres onto Snap Cbe grid paper and explain why they know each area is 15. ETA hand2mind

3 Extending the Activity 1. Have children add to the class collection by making two new shapes that look different bt have the same area. Have them keep track of the areas of the new shapes. 2. Take one shape of each area from the classroom set of pzzles. Have children pt them in order of area, from smallest to largest. Teacher Talk Where s the Mathematics? This activity gives children opportnities to see that shapes that look different may have the same area. Children se estimation to predict the area of a shape based on their nderstanding of the size of the face of a Snap Cbe. They se estimation again as they look throgh the class set of pzzles for shapes with matching areas. Children s early estimates will probably be jst gesses. As they find the areas of more shapes, they begin to develop estimation strategies. As they share their estimation strategies and listen to the strategies of their classmates, they start to see that estimates are more than mere gesses. Some estimation strategies may inclde comparing a shape to one whose area they have already fond or noting that certain longer figres may have areas that are close to those of more compact figres. Many children simply cont the Snap Cbes to find area. However, some may discover that conting in grops can save time. For example, in this figre, children who focs on colmns will see for 2s, for 3s, and two 4s. Those who focs on rows will see one 2, one 6, and two 10s. ETA hand2mind

4 3. Show the children a pzzle shape that they have not seen before. Have them compare the shape to other pzzle shapes whose areas they have already figred ot. Ask qestions abot the new shape sch as, Is it larger? smaller? and How is it the same? different? Ask children to se the answers to these qestions to estimate the area. Then have them se Snap Cbes to find the actal area. Some children may develop visal means of recognizing grops of nmbers. For example, they may organize their Snap Cbes in rows (or colmns) of different colors to facilitate finding area. The child who covered the shape shown below arranged the cbes into trains of for of one color and three of another color. This allows for skip-conting by 4s (4, 8, 12), then by 3s (3, 6, 9), then adding to find the area ( = 21). Other children may se a marker cbe in a different color to keep track of each tenth cbe they have conted Not all children are comfortable with the place-vale concepts that can help them with their conting. These children will need many experiences with groping sets of ten cbes before they are convinced that, for example, two grops of ten and one grop of twenty represent the same nmber. ETA hand2mind

5 PUZZLE SHAPES (AREA = 21) ETA/Cisenaire

6 PUZZLE SHAPES (AREA = 23) ETA

7 PUZZLE SHAPES (AREA = 25) ETA

8 PUZZLE SHAPES (AREA = 26) ETA

9 PUZZLE SHAPES (AREA = 28) ETA

10 SNAP CUBE GRID PAPER ETA