Objectives To review counting by 2s, 5s, and 10s; to extend this to counting by any number n; and to provide experiences with describing patterns that result from counting. 1 materials Teaching the Lesson Key Activities Children count by 2s, 5s, 10s, and by any number n from an arbitrary starting number, orally and with a calculator. They record and describe counting patterns on a number grid. Key Concepts and Skills • Count up and back by 2s, 5s, and 10s. [Number and Numeration Goal 1] • Skip count on a calculator. [Number and Numeration Goal 1] ⵧ Math Journal 2, p. 161 ⵧ Teaching Master (Math Masters, p. 195) ⵧ Teaching Aid Master (Math Masters, p. 415) ⵧ Transparency (Math Masters, p. 195; optional) ⵧ calculator ⵧ crayons • Record and discuss skip-counting patterns on a number grid. [Patterns, Functions, and Algebra Goal 1] See Advance Preparation Key Vocabulary multiple of 10 Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Number and Numeration Goal 1] 2 materials Ongoing Learning & Practice Children practice addition and subtraction facts using Fact Triangles. Children practice and maintain skills through Math Boxes and Home Link activities. 3 materials Differentiation Options READINESS Children correlate rhythmic counting by 2s, 5s, and 10s with different movements. ENRICHMENT EXTRA PRACTICE ELL SUPPORT Children find patterns on a five-column number chart. Children make patterns by coloring square and triangular grids. Children find multiples of 2, 5, and 10 on a five-column number chart. Additional Information Advance Preparation For the Part 1 activity Using a Calculator to Find Patterns on a Number Grid, make extra copies of Math Masters, page 195. You may also want to make an overhead transparency of this page. 544 Unit 7 Patterns and Rules ⵧ Math Journal 2, p. 162 ⵧ Home Link Master (Math Masters, p. 196) ⵧ , Fact Triangles ⵧ Teaching Master (Math Masters, p. 197) ⵧ Teaching Aid Master (Math Masters, p. 439) ⵧ crayons ⵧ counters (transparent preferred) ⵧ yellow and blue markers Technology Assessment Management System Math Message See the iTLG. Getting Started Mental Math and Reflexes Math Message 夹 Pose problems involving multiplication of equal groups. Suggestions: Isabel has 7 packages of cupcakes. There are 2 cupcakes per package. How many cupcakes in all? 14 cupcakes Jerome has 5 sheets of stickers. There are 8 stickers per sheet. How many stickers in all? 40 stickers Each lollipop costs 10 cents. Andrea bought 9. How much did she pay? $0.90 Start at 80 and count by 2s. Count as far as you can. Write your counts on an Exit Slip ( Math Masters, page 415). 1 Teaching the Lesson 䉴 Math Message Follow-Up WHOLE-CLASS ACTIVITY (Math Masters, p. 415) Ongoing Assessment: Recognizing Student Achievement Math Message 夹 Use the Math Message to assess children’s ability to count by 2s. Children are making adequate progress if they are able to count by 2s to 100. Some children may be able to count by 2s to numbers greater than 100. [Number and Numeration Goal 1] Have small groups or the whole class count by 2s from several 2-digit even numbers. Extend to counts from 3-digit numbers if children do well. Keep oral counting brisk and rhythmic. Ask volunteers to describe the pattern in counts by 2s. All counts are even numbers; the pattern of the ones digits repeats: 0, 2, 4, 6, 8, 0, 2, .... 0 8 2 6 4 When counting by 2s, the pattern of the ones digits repeats—0, 2, 4, 6, 8, 0, 2, .... Repeat with counts by 5s and 10s. For counts by 5s, begin with numbers that end in 0 or 5. For counts by 10s, begin with numbers that end in 0. Point out that when a number ends in 0 it is a multiple of 10. Each of the numbers in this 10 count is a multiple of 10. To support English language learners, discuss the meaning of multiple in this context. Encourage children to describe the patterns in these counts. Counts by 5s from numbers ending in 0 or 5 end in 0 and 5. Counts by 10s from numbers ending in 0 end in 0. Children may notice that numbers that end in 0 are also multiples of 2 and 5. Adjusting the Activity Ask children to count back, as well as up. In addition, have children discuss the pattern of counts by 10s starting from any number. As you count from one number to the next, the ones digit remains the same and the tens digit is increased by 1: 303, 313, 323, 333, .... If the tens digit is 9, then the tens digit becomes 0 and the hundreds digit is increased by 1: 393, 403, .... AUDITORY 䉬 KINESTHETIC 䉬 TACTILE 䉬 VISUAL Lesson 7 1 䉬 545 NOTE For skip counting on most calculators, number by which you want to count) = + n = + n = .... Remember that different calculators are “programmed” differently to handle skip counting. For example, for the first suggestion on the right: Press 22 + = = 3 WHOLE-CLASS ACTIVITY Calculator press s (the starting number) + n (the = 䉴 Skip Counting on the for the TI-108; Have a volunteer recall how to program calculators to count up by 2s, starting at 0, as the class follows along. (See margin note.) After children have programmed their calculators, have them press repeatedly, and slowly, while counting together by 2s. Try group counts by numbers other than 2, 5, and 10. Use such numbers as 3, 4, and 9. Children press the appropriate keys on their calculators as they count in unison. Suggestions: 䉯 Count from 22 by 3s. 25, 28, 31 ... Press 3 22 䉯 Count from 22 by 4s. 26, 30, 34 ... for the Casio SL-450. See Lesson 1-9 for 䉯 Count from 80 by 6s. 86, 92, 98 ... programming instructions for these two 䉯 Count from 180 by 9s. 189, 198, 207 ... calculator models. Adjusting the Activity Extend the range of numbers. A U D I T O R Y 䉬 K I N E S T H E T I C 䉬 T A C T I L E 䉬 V I S U A L Have volunteers record some of the counts on the board so the class can observe the patterns in the ones digits. You might find it helpful to circle the ones digits. 䉴 Using a Calculator to Find PARTNER ACTIVITY Patterns on a Number Grid (Math Journal 2, p. 161; Math Masters, p. 195) Student Page Date LESSON 7 1 䉬 Time Using a Calculator to Find Patterns 1. Use a calculator to count by 5s starting with the number 102. Color the counts on the grid with a crayon. Look for a pattern. 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 Have children use their calculators to solve Problem 1 on the journal page. Children count by 5s from the starting number 102. 107, 112, 117, 122, .... As children count with their calculators, they color the numbers on their number grids. You might choose to model this on an overhead transparency of Math Masters, page 195. Ask children to share any patterns they see. All numbers fall in two columns of the grid. The ones digit alternates between 2 and 7. 2. Pick a number to count by. Start with a number less than 310. Use your calculator to count. Record your counts on the grid with a crayon. Sample answers: 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 304 . Sample answer: The ones Here is a pattern that I found: digits are always even numbers. I counted by 6s starting with the number Math Journal 2, p. 161 546 Unit 7 Patterns and Rules Have children complete the journal page with a partner. Partners must first decide on a number to count by and then a starting number. Suggestions: 䉯 Children can select any number to count by, but encourage them to count by some number other than 2, 5, and 10. 䉯 Children can select any starting number less than 310. Student Page Partners write in their journals about any number patterns they observe for their count. When most of the children have completed the journal page, bring the class together to share and discuss the different patterns they found. Date Time LESSON Math Boxes 71 䉬 1. Which one is certain to happen? 2. Solve. Circle the best answer. 17 9 A. A spaceship will land at 27 9 school. NOTE Math Masters, page 195 is the same as journal page 161. Make extra copies of this page for children who finish early and want to repeat Problem 2 using different numbers. Extra copies are also useful for children who make an error and need to start again. 57 9 B. Your favorite sports team 68 88 will win every time. C. Spring will follow winter. Unit 8 18 48 77 9 97 9 D. You will be a movie star. 3. Make a 7-by-7 array with dots. How many in all? 49 4. Arrange the allowances in order from the minimum (smallest) to the maximum (largest). dots $10, $3, $7, $1, $4 $1 , $3 , $4 , $7 , $10 The minimum is $1 . The maximum is $10 . 2 Ongoing Learning & Practice 45 5. Match each person with the 䉴 Practicing with ⴙ, ⴚ Fact Triangles 6. How many boxes are on this correct weight. PARTNER ACTIVITY newborn Math Boxes page? 6 about 144 pounds 2nd grader about 63 pounds adult about 7 pounds boxes 1 How many boxes are on of 2 this page? 3 boxes Partners practice addition and subtraction facts. Math Journal 2, p. 162 䉴 Math Boxes 7 1 䉬 INDEPENDENT ACTIVITY (Math Journal 2, p. 162) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-3. The skill in Problem 6 previews Unit 8 content. Writing/Reasoning Have children draw, write, or verbalize their answers to the following: Describe any patterns you see in Problem 2. Sample answer: The ones digit is 8 in all the answers, and the tens digit is one less than the tens digit in the first number. Home Link Master 䉴 Home Link 7 1 䉬 INDEPENDENT ACTIVITY (Math Masters, p. 196) Home Connection Children count up from 3-digit numbers. They record some of their counts and look for patterns in their answers. Name Date HOME LINK 71 䉬 Family Note Time Count by 2s, 5s, and 10s In this lesson, your child has been counting by 2s, 5s, and 10s. After your child has completed these problems, help him or her look for patterns in the ones digits of the answers. In the example, the ones digits repeat: 0, 2, 4, 6, 8, 0, 2, 4, and so on. If your child is successful with these problems, ask him or her to count backward by 2s, 5s, or 10s. Start from a number that is a multiple of 10, such as 200. 96 Please return this Home Link to school tomorrow. Example: Count by 2s. Begin at 100. Write your first 10 counts below. 100 , 102 , 104 , 106 , 108 , 110 , 112 , 114 , 116 , 118 1. Count by 2s. Begin at 200. Write your first 10 counts below. 200 , 202 , 204 , 206 , 208 , 210 , 212 , 214 , 216 , 218 2. Count by 5s. Begin at 500. Write your first 10 counts below. 500 , 505 , 510 , 515 , 520 , 525 , 530 , 535 , 540 , 545 3. Count by 10s. Begin at 550. Write your first 10 counts below. 550 , 560 , 570 , 580 , 590 , 600 , 610 , 620 , 630 , 640 Look at your counts. Write about any patterns you find in the counts. Sample answers: In Problem 1, the ones digits repeat: 0, 2, 4, 6, 8, 0, 2, 4, …. In Problem 2, the ones digits repeat: 0, 5, 0, 5, …. In Problem 3, all the ones digits are 0. Math Masters, p. 196 Lesson 7 1 䉬 547 Teaching Master Name LESSON 71 䉬 Date Time 3 Differentiation Options Patterns on a Number Chart –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 READINESS 䉴 Counting by 2s, 5s, and 10s SMALL-GROUP ACTIVITY 5–15 Min To provide experience with counting, have children correlate rhythmic counting with a physical motion. For example: 䉯 1, 2 (clap), 3, 4 (clap), ... 䉯 1, 2, 3, 4, 5 (touch toes), 6, 7, 8, 9, 10 (touch toes), ... 䉯 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (jumping jack), ... ENRICHMENT 䉴 Exploring Patterns on a INDEPENDENT ACTIVITY 15–30 Min Number Chart Math Masters, p. 197 (Math Masters, p. 197) –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 To further explore patterns, have children use a five-column number chart. Children decide on a skip-count pattern, such as counting by 4s. They color the skip-count pattern on the number chart or use transparent counters to mark the numbers. They record the patterns they find. Have children describe their patterns using words like row, column, diagonal, left, right, skip, and so on. Sample answers: When counting by 4s, a diagonal pattern forms. Each time I go down a row I am counting by 5s. EXTRA PRACTICE Teaching Aid Master Name Date Time LESSON Making0 0Patterns Page Title 䉴 Making Patterns by INDEPENDENT ACTIVITY 15–30 Min Coloring Grids 䉬 Make designs by coloring the grids. Use more than one color in each design. (Math Masters, p. 439) Art Link Using at least two colors, children color a design on the square grid on Math Masters, page 439. They color a second design on the triangular grid. ELL SUPPORT 䉴 Finding Patterns in Multiples SMALL-GROUP ACTIVITY 5–15 Min of 2, 5, and 10 (Math Masters, p. 197) Math Masters, p. 439 548 Unit 7 Patterns and Rules To provide language support for multiples, have children use markers to color multiples of 2 in yellow and multiples of 5 in blue on a five-column number chart. Children should notice that multiples of 10 will appear green. Ask children to write lists of the first ten multiples of 2, 5, and 10. Have children write about the patterns they see.