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Name Master 1.1 Reasoning; Applying concepts shows understanding by demonstrating, explaining, and applying: – relationships in patterns – equivalence in Date Unit Rubric: Number Patterns Not Yet Adequate Adequate may be unable to demonstrate, explain, or apply: partially able to demonstrate, explain, and use: – relationships in – relationships in patterns – equivalence in simple numerical equations patterns Proficient appropriately demonstrates, explains, and uses: – relationships in patterns – equivalence in simple numerical equations – equivalence in simple numerical equations Excellent in various contexts, appropriately demonstrates, explains, and uses: – relationships in patterns – equivalence in simple and more complex numerical equations simple numerical equations Accuracy of procedures accurately identifies and applies pattern rules; extends number patterns finds the missing terms in an equation represents numbers to 10 000 often makes major errors in: makes frequent minor makes few errors in: errors in: – identifying pattern – identifying pattern rules rules – applying pattern – applying pattern rules rules – extending number – extending number patterns patterns – finding missing – finding missing terms in an terms in an equation equation – representing – representing numbers to numbers to 10 000 10 000 makes no errors in: may be unable to use appropriate strategies to solve and create problems that involve patterns with limited help, uses some appropriate strategies to solve and create problems that involve patterns; partially successful uses appropriate strategies to solve and create problems that involve patterns successfully uses appropriate, often innovative, strategies to solve and create problems that involve patterns successfully unable to explain reasoning and procedures clearly partially explains reasoning and procedures clearly explains reasoning and procedures clearly explains reasoning and procedures clearly, precisely, and confidently uses few mathematical terms appropriately uses some mathematical terms appropriately uses appropriate mathematical terms uses a range of appropriate mathematical terms with precision – identifying pattern – – – – Problem-solving strategies uses appropriate strategies to solve and create problems that involve number patterns; includes use of calculator Communication explains reasoning and procedures clearly uses appropriate language to describe number patterns (e.g., pattern rule, core, growing pattern, repeating pattern) rules applying pattern rules extending number patterns finding missing terms in an equation representing numbers to 10 000 – identifying pattern rules – applying pattern rules – extending number patterns – finding missing – terms in an equation representing numbers to 10 000 Copyright © 2004 Pearson Education Canada Inc. 27 Name Master 1.2 Date Ongoing Observations: Number Patterns The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning. STUDENT ACHIEVEMENT: Number Patterns Student Reasoning; Applying concepts Accuracy of procedures Problem solving Communication Explains and applies concepts related to: – identifying and extending patterns – equivalence Accurately identifies and extends a number pattern Finds missing terms in an equation Uses appropriate strategies to solve and create number pattern problems Uses appropriate language to describe number patterns Explains reasoning and procedures *Use locally or provincially approved levels, symbols, or numeric ratings. 28 Copyright © 2004 Pearson Education Canada Inc. Name Master 1.3 Performance Assessment Rubric: Calendar Patterns Not Yet Adequate Reasoning; Applying concepts shows understanding and ability to apply concepts by describing and explaining pattern rules Accuracy of procedures identifies and describes patterns accurately Problem-solving strategies uses appropriate strategies to identify and investigate number patterns on a calendar Communication uses appropriate mathematical terminology (e.g., pattern rule, core, growing pattern, repeating pattern) shows thinking clearly Date Adequate Proficient shows little understanding; may be unable to describe or explain pattern rules gives a partially appropriate description and explanation of pattern rules; may be vague or incomplete makes major errors in identifying and describing patterns makes frequent minor makes few errors in errors in identifying identifying and describing patterns and describing patterns makes no errors in identifying and describing patterns uses very limited strategies for investigating number patterns on a calendar; may rely only on those described in Steps 1 and 2 uses some appropriate strategies for investigating number patterns on a calendar including one that is not described (Step 3) uses appropriate and effective strategies for investigating number patterns on a calendar, including at least two that are not described (Step 3) uses innovative and effective strategies for investigating number patterns on a calendar, including at least two that are not described (Step 3) uses few appropriate mathematical terms uses some appropriate mathematical terms uses appropriate mathematical terms uses a range of appropriate mathematical terms clearly and precisely shows thinking clearly shows thinking clearly, precisely, and confidently unable to show thinking shows thinking with clearly some clarity gives an appropriate and complete description and explanation of pattern rules Excellent gives clear, appropriate, and detailed descriptions and explanations of pattern rules Copyright © 2004 Pearson Education Canada Inc. 29 Name Master 1.4 Date Unit Summary: Number Patterns Review assessment records to determine the most consistent achievement levels for the assessments conducted. Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying levels for each achievement category. Most Consistent Level of Achievement* Strand: Patterns and Relations Reasoning; Applying concepts Accuracy of procedures Problem solving Communication Ongoing Observations Strategies Toolkit (Lesson 6) Work samples or portfolios; conferences Show What You Know Unit Test Unit Problem: Calendar Patterns Achievement Level for reporting *Use locally or provincially approved levels, symbols, or numeric ratings. Self-Assessment: Comments: (Strengths, Needs, Next Steps) 30 Copyright © 2004 Pearson Education Canada Inc. OVERALL Name Master 1.5 Date To Parents and Adults at Home … Your child’s class is starting a mathematics unit on number patterns. From traffic to petals on a flower—patterns are how we make sense of the world around us. Patterns occur regularly in mathematics. As children learn to analyse patterns, they develop powerful reasoning skills that will help them make sense of mathematics and science. In this unit, your child will: Use charts to display patterns. Identify the rule for a number pattern. Extend number patterns. Create number patterns. Use patterns to solve problems. Investigate equations. Patterns occur in many different forms. Encourage your child to look for patterns around the home, and talk about them. You may find regular repeating patterns—maybe you mark the calendar to remind you of soccer practice every week. Other patterns may be growing or shrinking—the number of cookies remaining in the jar, if it’s “take one at a time.” Here’s a game you can play with your child that creates a growing pattern of words. Growing List Word Game Think of words to describe a cat or other animal. Each player repeats the words said by previous players in the correct order, and adds a new word at the end of the list. The first player starts by saying, for example, “My cat is an adorable cat.” The next player must repeat this but add a new descriptive word. For example, “My cat is an adorable, black cat.” A player is out of the game when he or she cannot repeat the list or fails to provide a new word. Copyright © 2004 Pearson Education Canada Inc. 31 Name Calendar Page SUNDAY MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY Master 1.6 32 Copyright © 2004 Pearson Education Canada Inc. Date Name Master 1.7 Date Additional Activity 1: Number Search Work on your own. Use a hundred chart. Choose a number less than 50. Circle the number on your hundred chart. Add 10 to your number. Where did you land on the chart? Start at the same number. Add 20. Where did you land on the chart? Start at the same number. Add 30. Predict where you will land on the chart. Describe how you can use patterns in a hundred chart to add 10, 20, or 30 to a number. How could you add 40 or 50 to a number? Take It Further: Describe how you can use patterns in the hundred chart to add 9, 18, or 27 to a number. Copyright © 2004 Pearson Education Canada Inc. 33 Name Master 1.8 Date Additional Activity 2: Patterns to the Nines Work on your own. You will need a calculator. Look at the 3 products in List A. What patterns do you see? Use the patterns to predict the next 3 products. Check your predictions with a calculator. How can you extend the pattern? Use a calculator to check. Repeat the activity for List B. List A List B 3 x 9 = 27 99 x 12 = 1188 3 x 99 = 297 99 x 23 = 2277 3 x 999 = 2997 99 x 34 = 3366 3 x 9999 = _____ 99 x 45 = ____ 3 x 99 999 = _____ 99 x 56 = ____ 3 x 999 999 = _____ 99 x 67 = ____ Take It Further: Use a calculator to find other patterns with nines. 34 Copyright © 2004 Pearson Education Canada Inc. Name Master 1.9 Date Additional Activity 3: Twenty-One Work with a partner. Use 21 Snap Cubes. The goal is to make the other player remove the last cube. How to play: Join 21 Snap Cubes to form a chain. Take turns to remove 1, 2, or 3 Snap Cubes from the chain. The player who removes the last cube loses the game. Play the game several times. Discuss any patterning strategies you used to win. Take It Further: Play Twenty-One by removing 2, 3, or 4 cubes each time. Copyright © 2004 Pearson Education Canada Inc. 35 Name Master 1.10 Date Additional Activity 4: Make It Work Work with a partner. Use Pattern Blocks. Find the value for each block that makes each statement an equation. The same blocks represent the same number. Each different block represents a different number. + = 20 + = 15 Take It Further: Create your own number puzzle with Pattern Blocks. Trade puzzles with your partner. Solve your partner’s puzzle. 36 Copyright © 2004 Pearson Education Canada Inc. Name Master 1.11 Date Step-by-Step 1 Lesson 1, Question 4 Step 1 Fill in the missing numbers on this 5-wide hundred chart. 1 2 3 6 7 8 11 9 14 17 24 26 27 30 33 36 38 35 39 42 45 48 Step 3 Count on by 5s. Shade these numbers with a second colour. 51 55 56 57 59 62 Step 4 Start at 8 and count on by 10s. Shade these numbers with a third colour. 63 67 69 71 74 76 ________________________________ ________________________________ Step 7 How are the patterns different? ________________________________ ________________________________ 75 78 82 Step 5 Use this 10-wide hundred chart. Repeat the number patterns from Steps 2, 3, and 4. Step 6 How are the patterns in the two charts the same? ________________________________ 15 19 21 Step 2 Count on by 2s. Shade these numbers with one colour. 5 86 90 96 98 100 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 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ________________________________ Copyright © 2004 Pearson Education Canada Inc. 37 Name Master 1.12 Date Step-by-Step 2 Lesson 2, Question 4 Step 1 Here is a number pattern: 5, 8, 11, 14, 17 Is this a growing pattern? ________________________________________________________________ How do you know? ________________________________________________________________ What is the pattern rule? ________________________________________________________________ Step 2 Continue this pattern: 5, 15, 25, 35, ___, ___, ___ Is this a growing pattern? ________________________________________________________________ What is the pattern rule? ________________________________________________________________ Step 3 Use 5 as a start number. Write your own growing pattern. 5, ___, ___, ___, ___, ___ What is the pattern rule? ________________________________________________________________ 38 Copyright © 2004 Pearson Education Canada Inc. Name Master 1.13 Date Step-by-Step 3 Lesson 3, Question 5 Step 1 12 + 21 How are 12 and 21 different? How are they the same? ___________________________________ 12 13 14 ___ ___ ___ ___ + + + + + + + 21 31 41 ___ ___ ___ ___ = = = = = = = ___ ___ ___ ___ ___ ___ ___ Step 2 Continue the pattern. Fill in the blanks. Find each sum. Step 3 Write a rule for the pattern in the sums. _______________________________________________________ _______________________________________________________ Step 4 The next statement is 19 + 91. Find the sum. ___________________ Step 5 What would the next statement be? Find the sum. _______________ Step 6 Does the pattern rule in Step 3 always work? ___________________ Explain your answer. _______________________________________________________ _______________________________________________________ Copyright © 2004 Pearson Education Canada Inc. 39 Name Master 1.14 Date Step-by-Step 4 Lesson 4, Question 5 Step 1 Find the sum: 5 + 4 = ___ Step 2 Write two different numbers that have the same sum as in Step 1. ___ + ___ = ___ Step 3 What other pairs of numbers have the same sum as in Step 1? 5 + 4 = ___ + ___ 5 + 4 = ___ + ___ 5 + 4 = ___ + ___ 5 + 4 = ___ + ___ Step 4 How do you know when you have found all the pairs of numbers with the same sum? _______________________________________________________ _______________________________________________________ _______________________________________________________ Step 5 Repeat Steps 1 to 4 with each pair of numbers. b) 8 + 7 = ___ c) 10 + 3 = ___ 40 Copyright © 2004 Pearson Education Canada Inc. d) 16 + 2 = ___ Name Master 1.15 Date Step-by-Step 5 Lesson 5, Question 5 Step 1 Find the difference: 18 – 6 = ___ Step 2 Write two different numbers that have the same answer as in Step 1. ___ – ___ = ___ Step 3 What other pairs of numbers have the same answer as in Step 1? 18 – 6 = ___ – ___ 18 – 6 = ___ – ___ 18 – 6 = ___ – ___ How did you find the numbers? __________________________________________________ __________________________________________________ __________________________________________________ Step 4 Repeat Steps 1 to 3 for 20 – 3 = ___ – ___ . Copyright © 2004 Pearson Education Canada Inc. 41 Name Master 1.16 Date Unit Test: Unit 1 Number Patterns Part A 1. Use 1-cm grid paper. Make a 6-wide number chart from 1 to 48. This chart will have 8 rows. a) What patterns do you see in the rows? Columns? Diagonals? b) Start at 4. Shade every 5th number. Describe the position pattern. c) Write a rule for the number pattern you shaded. Use the rule to find the next 6 numbers in the pattern. 42 Copyright © 2004 Pearson Education Canada Inc. Name Master 1.16b Date Unit Test continued 2. a) Find the pattern rule for this pattern. Write the next 3 terms. 67, 61, 55, 49, ___, ___, ___ b) Look at the pattern in part a. Add 1 to each number. Write the first 5 terms in this pattern. Write the new pattern rule. c) Look at the pattern in part a. Use the same start number. Subtract 1 from the number you take away. Write the first 5 terms in this pattern. Write the new pattern rule. Part B 3. Find all the pairs of numbers that make this statement an equation. 11 + 3 = ___ + ___ Use a pattern rule so you know when you have found all possible ways. Copyright © 2004 Pearson Education Canada Inc. 43 Name Master 1.16c Date Unit Test continued 4. Each figure represents a different number. Find the number that each figure represents. + + = 11 8 = + Explain how you solved the problem. Part C 5. Write as many different patterns as you can that begin with 1, 2, 3. Tell about each pattern you write. 44 Copyright © 2004 Pearson Education Canada Inc. Name Master 1.17 Date Sample Answers Unit Test – Master 1.16 Part B Part A 1. a) b) c) 2. a) b) c) As you go across a row, each number increases by 1. As you go down a column, each number increases by 6. In a diagonal going down and to the right, each number increases by 7. In a diagonal going down and to the left, each number increases by 5. Start at 4. Go down 1 square, then 1 square left. Then start at 24 and go down 1 square, then 1 square left. Start at 4. Count on by 5. 49, 54, 59, 64, 69, 74 43, 37, 31 Rule: Start at 67. Subtract 6 each time. 68, 62, 56, 50, 44 Rule: Start at 68. Subtract 6 each time. 67, 62, 57, 52, 47 Rule: Start at 67. Subtract 5 each time. 3. I can do this 7 ways. 11 + 3 = 14, so I begin with 0 + 14. I added 1 to the first number and subtracted 1 from the second number until I reached 6 + 8. 0 + 14; 1 + 13; 2 + 12; 3 + 11; 4 + 10; 5 + 9; 6+8 If I continue, I would get the same pairs of numbers, but in reverse order. 4. Square = 3, triangle = 5 The 1st equation is 2 squares and 1 triangle make 11. The second equation is 1 square and 1 triangle make 8. So, the extra square in the 1st equation is 11 – 8 = 3. So, in the 2nd equation, if the square is 3, then the triangle is 5. I tried 3 and 5 in the first equation and they worked. Part C 5. 1, 2, 3, 4, 5, 6, … This is a growing pattern that increases by 1 each time. 1, 2, 3, 1, 2, 3, 1, 2, 3, … This is a repeating pattern with a core: 1, 2, 3. 1, 2, 3, 3, 2, 1, 1, 2, 3, 3 ,2, 1, … This is a repeating pattern with a core: 1, 2, 3, 3, 2, 1. 1, 2, 3, 5, 7, 10, 13, 17, 21, … This is a growing pattern where you start at 1, add 1 two times, then add 2 two times, then add 3 two times, and so on. Copyright © 2004 Pearson Education Canada Inc. 45 Extra Practice Masters 1.18–1.21 Go to the CD-ROM to access editable versions of these Extra Practice Masters. 46 Copyright © 2004 Pearson Education Canada Inc.