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Problem Solving Steps Step 1. Step 2. Step 3 Step 4 Step 5 Step 6 Read information carefully Understand what the question is asking you do to. Use information from the question to find your answer Decide on a strategy to use. Show your thinking Write a final statement (sentence) Strategies Use a pattern Use logic Work backwards Make a picture or a table Draw a chart or a graph Use a model Make an organized list Solve a simpler problem MATH UNIT 1 – NUMBER PATTERNS Learning Goals (gr. 5) I can find a pattern rule for a number pattern I can identify, extend, and create patterns I use patterns to pose and solve problems Learning Goals (gr. 6) I can write a pattern rule for a number pattern I can identify, extend, and create patterns I use patterns to pose and solve problems I can describe and model patterns I use patterns in a table to make predictions I use patterns to explore divisibility rules I can find the value of a missing number in an equation I use patterns to explore integers Patterning Vocabulary REPEATING PATTERN = a pattern that repeats e.g. 4, 8, 4, 8, 4, 8 PATTERN CORE = the part of the pattern that repeats e.g. 4, 6, 4, 6, 4, 6, 4,6 4,6 is the core. GROWING PATTERN = a pattern that gets bigger e.g. 2, 4, 6, 8, 10 SHRINKING PATTERN = a pattern that gets smaller e.g. 50, 45, 40, 35, 30 PATTERNING RULE = the math function (+, -, x, / ) to follow. To follow the pattern. Start at ___________________. Add _____________ each time. Increase (UP) the number you add (+) by ____________ each time Decrease (DOWN) the number you subtract (-) by ____________ each time Alternately – switch back and forth e.g. add 1, subtract 2, each time. Number Patterns and Pattern Rules - strategies To identify the pattern rule, I find the difference between pairs of consecutive numbers in the pattern. 5 (+1) 6 (+2) 8 (+3) 11 (+4) 15 The pattern rule is: Start at 5. Add 1. Increase the number you add by 1 each time. To get the next 5 terms, continue to increase the number you add by 1 each time. 5,6,8,11,15,20,26,33,41,50… 2 (+3) 5 (+4) 9 (+3) 12 (+4) 16 The pattern rule is: Start at 2. Alternately add 3, then add 4. To get the next 5 terms, continue to add 3, then add 4. 2,5,9,12,16,19,23,26,30,33… 10 (-4) 6 (+5) 11 (-4) 7 (+5) 12 The pattern rule is: Start at 10. Alternately subtract 4, then add 5. To get the next 5 terms, continue to subtract 4, then add 5. 10,6,11,7,12,8,13,9,14,10… Patterning vocabulary and definitions Input/Output Machine performs an operation (=add/subtract/divide by/multiply by) on a number (the input) to produce another number (the output). An operation is add, subtract, multiply or divide. This input/output machine multiplies the input by 2. Input operation 6 X2 output 12 What are multiples? Start at a number, then count on by that number to get the multiples of that number. To get the multiples of 3, start at 3 and count on by 3. 3,6,9,12,15,… Patterning vocabulary and definitions (gr. 6) This input/output machine doubles each input, then adds 6. When the input is 1, the output is 8. When the input is 4, the output is 14. Input operation operation Output 1 X2 2 +6 8 4 X2 8 +6 14 I check all the inputs to make sure I have found the correct numbers and the correct operations!!! (Gr. 6) What is a recursive pattern? In a recursive pattern, each term can be foundby applying the pattern rule to the previous term. Ex. Write the first 5 terms for a recursive pattern that starts at 7. A pattern rule is: Start at 7. Multiply by 2, then add 1 each time. 7 x 2 + 1 = 15 15 x 2 + 1 = 31 31 x 2 + 1 = 63 63 x2 + 1 = 127 The first 5 terms of the pattern are: 7, 15, 31, 63, 127 Here is a recursive pattern: 1, 6, 11, 16, 21 To find the pattern rule, find the difference between each pair of consecutive terms. The difference between each pair of consecutive terms is 5. Add 5 to each term to find the next term. 1 (6-1=5) 6 (11-6=5) 11 (16-11=5) 16 (21-16=5) 21 Patterning vocabulary and definitions (gr. 6) Number Patterns Divisibility Rules: A whole number is divisible by: 2 = if it is an even number 3 sum of digits is divisible by 3 (The numbers that are divisible by 3 are multiples of 3) 4 if the number represented by the tens and ones digits is divisible by 4 (every multiple of 4 is divisible by 4) 5 last digit (the ones digit) is 0 or 5 6 if the number is divisible by 2 and by 3 8 if the number represented by the hundreds, tens, and ones digits is divisible by 8 9 if the sum of the digits is divisible by 9 10 if the ones digit is o Patterning vocabulary and definitions (Gr. 6) An equation is a statement that two things are equal. e.g. 7 x 3 = 21 19 = 25-6 You solve an equation when you find the value of a missing number in an equation. e.g. 163 = ? + 49 You can use an inverse operation to find the missing number 163 – 49 = ? (?=114) e.g. ? divided by 6 = 144 The inverse operation here is multiplication. The number that is divided by 6 to get 144 = 144 x 6 = 864. This means that your answer is 864 divided by 6 = 144. Your solution is 864. Multiplication and division are inverse operations. Addition and subtraction are also inverse operations. Patterning vocabulary and definitions (gr. 6) Numbers such as 24 and -18 are integers. You can represent integers on a number line. The number line may be vertical (as in a thermometer) or horizontal (the number line to the left of 0 shows negative numbers). You use integers to represent quantities that have both size and direction. Hilde spent $ 25.00. This can be represented as - $ 25. Tammy walked 5 steps forward. This can be represented at + 5 steps, or 5 steps. Shannon swam to a depth of 50 m. This can be represented as - 50 m. NOTE: If no sign is written, the integer is positive! Strategies to use when you are stuck on a math problem Prepare for success!!!! GET UNSTUCK! HOW??? Represent the information in another way. Rewrite the question in your own words. Reorganize the information. Draw a diagram or use a table. Think about what you already know. Ask yourself: What facts am I given? What other problem have I done like this one? What do I know how to do that might help? What possible answers can I eliminate? Try a problem-solving strategy draw a diagram/make a table/use a pattern Collaborate (ask two friends or Madame Acx) – unless it is a test, of course!