COVER THE CATERPILLAR

Transcription

1 COVER THE CATERPILLAR NUMBER PATTERNS/FUNCTIONS Conting Eqivalence Patterns Getting Ready What Yo ll Need Pattern Blocks, at least 6 yellow, 20 ble, and 40 green per pair Cover the Caterpillar otlines, page 90 Crayons Overview Children find combinations of ble and green Pattern Blocks that can be sed to cover for yellow hexagons. In this activity, children have the opportnity to: se patterns to solve a problem work with eqivalence in a geometric context The Activity Introdcing Ask children to find a way to cover their yellow Pattern Block sing exactly 4 blocks. Confirm that the only combination that works is 2 ble blocks and 2 green blocks. Record this finding on the board: Nmber of Ble Nmber of Green Total Nmber Now ask children to cover the hexagon sing exactly 5 blocks. Again, elicit that there is only one soltion: 1 ble block and 4 green blocks. Add this information to the chart. Nmber of Ble Nmber of Green Total Nmber

2 On Their Own How many different ways can yo se only ble and green Pattern Blocks to cover the caterpillar? Work with a partner. Pt 4 yellow blocks together to make yor caterpillar so it looks like this: Use only ble and green Pattern Blocks to cover yor caterpillar. Record yor soltion by coloring the caterpillar otline. Keep track of the nmber of ble blocks yo sed and the nmber of green blocks yo sed. Also keep track of the total nmber of blocks yo sed. Now se different nmbers of ble and green blocks to cover the caterpillar. Record these reslts. Repeat the activity several times. Look for patterns in yor work. The Bigger Pictre Thinking and Sharing Invite children to discss how they worked on the activity. Then have them help yo create a class chart with the headings Nmber of Ble Blocks, Nmber of Green Blocks, and Total Nmber of Blocks. Patterns may be easier for children to see if yo arrange their data in order by the total nmber of blocks sed. Use prompts sch as these to promote class discssion: How many different combinations of ble and green blocks did yo find that will cover the caterpillar? What is the greatest nmber of blocks that anyone sed? What is the least? What strategies did yo se for solving this problem? Did yo change strategies as yo worked? If so, how did yo change, and why? Did yo notice any patterns that helped yo find soltions? Is so, describe them. Do yo think or class chart incldes all of the soltions? If not, which ones do yo think might be missing? Illstrate data in the chart with children s colored-in caterpillars.

3 Extending the Activity 1. Ask children to repeat the activity for a caterpillar made of six hexagons and compare the reslts with those for the for-hexagon caterpillar. Teacher Talk Where s the Mathematics? There are a variety of ways in which children investigate this problem. Some may se trial and error. Others may begin by trial and error and then develop a systematic approach. No matter what strategies they choose, children find that there are many different combinations of ble and green blocks that can be sed to cover the caterpillar, and that they mst do lots of conting. Children may begin their search for soltions by covering the hexagons sing only ble parallelograms. This will reqire 12 blocks, the smallest nmber of total blocks needed. They may then find additional soltions by sbstitting two green triangles for each ble parallelogram. Other children may begin the other way by covering the hexagons entirely with green triangles. They may realize that this arrangement will tilize the largest nmber of blocks (24). They may then sbstitte one of the ble parallelograms for two green triangles to make a new soltion. After children have sed this sbstittion strategy several times, they may be able to fill in the chart withot actally working with the blocks becase they have fond a pattern. This chart shows the 13 soltions: Ble Green Total

4 2. Present other problems in which children mst cover a particlar set of blocks with a specified nmber of other blocks of two or three colors. When children are asked to describe the patterns they notice, they are apt to point ot that as the nmbers in the ble colmn increase by one, the nmbers in the green colmn decrease by two. This describes what was happening when they traded in two triangles for one parallelogram. They may also notice that the nmbers in the total colmn decrease by one. This happens becase every time they trade in two triangles for one parallelogram, they have one less piece left on the caterpillar. Others may note that the nmber of green blocks is always an even nmber, the the nmber of ble blocks cold be either even or odd. If the class has not discovered all the soltions and there are holes in the chart, they may be able to predict what soltions are missing, and then se the Pattern Blocks to verify them. When the patterns appear to be complete, it is likely that the chart contains all of the possible soltions. As they search for patterns and organize the data into a chart, children come to see how these strategies can be sefl in solving problems. Helping children to relate the changes in the nmbers back to what they were doing with the Pattern Blocks in the activity, enables them to recognize the connection between their work and the reslting mathematics.

5 COVER THE CATERPILLAR OUTLINES