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Instructional Strategies
MAP2D Trimester 1 Instructional Strategies Grade 5 Updated 6/10 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Round Numbers! Long Beach Unified School District has , 572 students enrolled. Round this to the nearest __________. Underline the word that comes after “nearest”. Underline the digit in the indicated place. Circle the digit to the right of the underlined place. If the circled digit is 5 or greater, add one to the underlined place and change all digits to the right to zeros. or If the circled digit is 4 or less, keep the underlined place and change all digits to the right to zeros. Ch. 1 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Round Numbers! Example: What is 45,638 rounded to the nearest thousand? 4 or less, stays the same 5 or higher, add one more 45,500 45,000 46,000 45,638 On the number line, 45,638 is between 45,000 and 46,000 but is closer to 46,000. 45, 6 38 46,000 Ch 1 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Two hundred fifty-seven AND forty-four hundredths
Let’s Round Numbers ! 2 5 7 4 3 8 tens hundredths thousandths thousands hundreds tenths ones Example: What is rounded to the nearest hundredths? Two hundred fifty-seven AND forty-four hundredths Ch 2.1 & Ch 11.1 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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CHECK to see the answer is close to the estimate
Let’s Add Decimals! hundredths tenths PROBLEM: = tens ones ESTIMATE as = 18 REWRITE the expression vertically, line up by place value and decimals FILL IN the empty spaces with zeros 17.94 is close to 18 PLACE the decimal point in the sum CHECK to see the answer is close to the estimate ADD Ch & 2.1 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Subtract Decimals!
hundredths tenths PROBLEM: – 3.2 = ones ESTIMATE as 9 – 3 = 6 REWRITE the expression vertically, line up by place value and decimals FILL IN the empty spaces with zeros 5.75 is close to 6 PLACE the decimal point in the difference CHECK to see the answer is close to the estimate SUBTRACT Ch & 2.1 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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0.6 or 0.60 100 60 10 6 = 0.6 is equal to 0.60 Equal Decimals!
Which decimal is greater? 0.6 or 0.60 READ THEM CORRECTLY like reading fractions 100 60 10 6 = WRITING ZEROS to the right of non-zero digits does not change the value of the decimal. This is why you can fill in zeros when adding or subtracting decimals. 0.6 is equal to 0.60 Ch. 11 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Solve Algebraic Equations
Use inverse operation to find the missing variable. Ch. 14 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Solve Algebraic Equations
Use inverse operation to find the missing variable. Ch. 14 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Solve Equations Use inverse operation to find the missing variable. Ch. 14 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Why the Zero Place Holder?
PROBLEM: 23 X 45 MULTIPLY by the ones digit “5” MULTIPLY by the tens digit “4” The 4 represents 40. When you multiply by a multiple of 10 you have a zero in the ones place. It’s All About the Facts Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Multiply Decimals!
PROBLEM: x 4.5 = ESTIMATE as 12 x 5 = 60 REWRITE the expression vertically MULTIPLY the numbers as if they were whole numbers UNDERLINE the digits to the right of the decimal in the multiplication problem UNDERLINE the same number of digits in the answer that were underlined in the problem PLACE the decimal in front of the last digit that was underlined 55.35 is close to 60 CHECK to see the answer is close to the estimate Ch. 12 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Multiply Decimals with ZEROS in the Product!
PROBLEM: x 0.5 = ESTIMATE as 0 x 1 = 0 REWRITE the expression vertically MULTIPLY the numbers as if they were whole numbers UNDERLINE the digits to the right of the decimal in the multiplication problem UNDERLINE the same number of digits in the answer that were underlined in the problem; fill in empty spaces with zeros 0.085 is close to 0 PLACE the decimal in front of the last digit that was underlined CHECK to see the answer is close to the estimate Ch. 12 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Do Long Division! No Yes
How many times does 25 go into 1678? No idea… Let’s use a shorter problem! Does the 2-digit divisor go into the 1st two digits of the dividend? (Does 25 go into 16?) No UNCOVER the next digit in the dividend. (Does 25 go into 167?) Yes Ch. 4 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Do Long Division! x 8
How many times does 25 go into 167? ESTIMATE by covering the 5 and 7 with your finger. 2 times what is close to 16? This is your first estimate. Ch. 4 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Do Long Division! x 6 x 7 x 8 No No Yes CHECK the 8:
TRY AGAIN: No TRY AGAIN: Yes Ch. 4 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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8 6 7 - 150 178 - 175 3 3 Let’s Do Long Division! FINISH
R3 FINISH 8 Look back at your work to help you solve the problem! - 150 178 - 175 3 3 Ch. 4 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Solve Division Problems with Remainders
When you solve a division problem, sometimes you need to decide how to interpret the remainder. Sometimes you use the REMAINDER to decide on the answer. Example: The craft club members made 19 puppets. They want to package the puppets 5 to a box. How many boxes will they need? 3 R4 There will be 3 full boxes. Another box is needed for the 4 extra puppets. So 4 boxes are needed in all. -15 4 Ch 13 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Solve Division Problems
When you solve a division problem, you can write the remainder as a fraction. Sometimes you write the remainder as a FRACTION. Example: The craft club made 6 picture frames. If they used 19 feet of framing material, how much material did each frame require? Each frame required 3 feet of framing material. - Ch 13 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Solve Division Problems When you solve a division problem, you can write the remainder as a decimal. 30 5 PROBLEM: = x REWRITE 12 into 366 -36 DIVIDE like regular whole numbers 6 If there is a remainder, place a decimal and a zero in the dividend -0 6 0 -6 0 Bring up the decimal in the quotient and continue to divide Ch. 13 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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$ 2 - 8 1 8 - 1 6 - 2 0 4 5 Let’s Divide Money PROBLEM: $9.80 4 =
$ 2 - 8 1 8 - 1 6 - 2 0 4 5 PROBLEM: $9.80 4 = REWRITE 4 into $9.80 WRITE the dollar sign and decimal in the quotient DIVIDE Ch. 13 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Divide Decimals PROBLEM: 4.48 0.08 = REWRITE 0.08 into 4.48
MOVE decimals 2 places right by multiplying divisor and dividend by 100 DIVIDE PLACE the decimal point in the quotient Ch. 13 L 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Multiply or Divide from Left to Right
Order of Operations Parentheses Exponents Multiply or Divide from Left to Right Add or Subtract from Left to Right Ch. 14 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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PROBLEM: Simplify 22 – 4 2 + 2 3
Order of Operations PROBLEM: Simplify 22 – 4 3 Parentheses 22 – 4 3 (there are none here) Exponents 4 – 4 3 (perform 2 squared first) 4 – Multiply or Divide from Left to Right (divide 42 and multiply 23) Add or Subtract from Left to Right 8 (subtract 4-2, then add 6) Ch 14 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Simplify Expressions
Parentheses First Multiplication or Division from Left to Right 60 – 3 x 18 Add or Subtract from Left to Right 6 Ch. 14 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Evaluate Expressions
Substitute for the variable 4 x (5 + 15) 80 Parentheses First 4 x 20 Multiplication or Division from Left to Right (No Addition or Subtraction) Ch. 14 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Evaluate Expressions
m = 6 (10 + m) 4 (10 + 6) 4 4 Substitute for the variable Parentheses First Multiplication or Division from Left to Right (No Addition or Subtraction) Ch. 14 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Evaluate Expressions
59 Substitute for the variable (No Parentheses) 54 + 5 Multiplication or Division from Left to Right Add or Subtract from Left to Right Ch. 14 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Step 1 Step 2 Step 3 Let's Solve Equations Undo multiplication
Simplify Step 3 Check Ch 14 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Step 1 Step 2 Step 3 Let's Solve Equations Undo multiplication
Simplify Step 3 Check Ch 14 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Step 1 Step 2 Step 3 Let's Solve Equations Undo Division Simplify
Check Ch 14 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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The Distributive Property
PROBLEM: 4(x + 3) Four is multiplying the quantity “x + 3” That means four will multiply both the x and the 3! 4 times x 4 times 3 4(x + 3) 4x + 12 Multiply 4 times x Copy the operation sign Multiply 4 times 3 Ch. 14 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Use Distributive Property to Find the Missing Variable
Cross out matching numbers on both sides of the equal sign Circle what is left Problem: 5 x 36 = (5 x 30) + (5 x n) 5 x 36 = (5 x 30) + (5 x n) n = 6 30 + 6 Problem: 6 x 25 = (6 x m) + (6 x 5) 6 x 25 = (6 x m) + (6 x 5) 20 + 5 m = 20 Ch 15 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Use Distributive Property to Find the Missing Variable
Problem: 8 x m = (8 x 40) + (8 x 7) 8 x m = (8 x 40) + (8 x 7) m = 47 Problem: 33 x 62 = 33 x ( p + 2) 33 x 62 = 33 x ( p + 2) 60 + 2 p = 60 Ch 15 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Prime Numbers What are the first seven prime numbers? 2, 3, 5, 7, 11, 13, 17 One is NOT PRIME because it does not have exactly two factors. One is NOT COMPOSITE because it does not have more than two factors. Ch. 5 L 1 & 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Factor and Use Exponents!
PROBLEM: Write the prime factorization of 56. What are 2 factors with a product of 56? 56 Circle the PRIME FACTORS and… 7 8 Continue to factor any COMPOSITE NUMBERS. 2 4 Continue until only prime numbers remain. 2 2 Write prime factorization in exponential form. 56 = 23•7 Ch. 5 L 5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Complete the Equivalent Fractions!
Hint: Little goes after big! Think: “4 times what equals 24?” Since 4 x 6 = 24, we will also multiply the numerator by 6. 18 x 6 x 6 Think: “3 times what equals 15?” Since 3 x 5 = 15, then “5 times what equals 25?” So 5 is the missing number. x 5 5 x 5 Ch 6 L 1 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Simplify Fractions!
2 5 6 1 PROBLEM: Simplify REWRITE both the numerator and denominator using prime factors DIVIDE OUT common factors (CANCEL) Multiply the remaining numbers for the simplified fraction 3 x Ch. 6 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Tips for Recognizing Simplified Fractions
When the numerator and denominator are CONSECUTIVE numbers the fraction is in simplest form. and many more! When the denominator is PRIME the fraction is in simplest form. and many more! MAP2D Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Tips for When to Simplify a Fraction
You must simplify a fraction if both numbers are EVEN. and many more! You must simplify a fraction if the denominator is DIVISIBLE by the numerator. and many more! MAP2D Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Convert Mixed Numbers to Improper Fractions!
FIRST multiply denominator by the whole number FIRST 3 x 4 How many thirds are in the whole number? 3 x 4 = 12 1 2 3 4 5 6 7 8 9 10 11 12 NEXT PLUS how many thirds are in the fraction? NEXT 12 + 2 = 14 14 TOTAL THIRDS = add the product to the numerator 13 14 = LAST The sum is the numerator 3 Keep the same denominator Ch 6 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Convert Improper Fractions to Mixed Numbers!
2 1 5 3 = = 5 3 3 3 1 2 1 Improper Fraction Mixed Number Divide Ch 6 L 3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 Section 3-4
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. Let's Convert Fractions to Decimals ! Now Divide
First, add a decimal and write 2 zeros. Next, put a decimal in the quotient. . Now Divide Ch. 6 L 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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“One fourth is equal to twenty-five hundredths”
Let's Convert Fractions to Decimals ! 8 2 0 = 0.25 START HERE Decimal 1 “One fourth is equal to twenty-five hundredths” OR “One quarter is worth twenty-five cents” Fraction = 0.25 Ch. 6 L 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let's Convert Decimals to Fractions !
2.Simplify the fraction using prime factorization. 1 1.Write the decimal as a fraction. Ch. 6 L 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Relating Fractions and Decimals
4 2 5 tens hundredths Decimal point hundreds ones tenths 4.2 5 = (OR 4 ) Four and twenty-five hundredths Ch. 6 L 6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Mixed Numbers on the Number Line
A M T H 8 9 10 11 Let’s Find Point A on the Number Line: Write down the whole number to the left of your point. Count the spaces between the two numbers and that is the denominator for the fraction. Count the spaces between the whole number and your point and that is the numerator for the fraction. Point A is located at Ch.6 L 7 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Mixed Numbers on the Number Line
A M T H 8 9 10 11 Example: What number does Point T represent on the number line? Point T is located at Ch.6 L 7 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Add Fractions! 2 6 3 Yes
When the denominators are the same, add the numerators: 1 2 6 3 Yes Can we simplify? Use prime factors Ch. 7 L 2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Add Fractions! No Yes PROBLEM: Can we add these as they are?
Why not? They have unlike denominators. TO FIND A COMMON DENOMINATOR: First ask if one denominator goes into the other. Does 3 go into 12 evenly? Yes We will use 12 as the common denominator. Ch. 8.4 & 8.5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Add Fractions! + 2 6 3 Yes
x 1 x 4 + Multiply numerator and denominator by the same number REWRITE and ADD 2 6 3 1 SIMPLIFY if possible Yes Can we simplify? Ch. 8.4 & 8.5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Add Fractions! PROBLEM: Multiply denominators to find common denominator x 3 x 2 Multiply numerator and denominator by the same number REWRITE and ADD SIMPLIFY if possible Can we simplify? No 5 and 6 are consecutive Ch. 8.4 & 8.5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Use the Ladder to Find the Least Common Denominator (LCD)!
Example: 8 2 12 WRITE the two denominators on one line 2 4 6 Draw a step in the shape of an “L” 2 3 DIVIDE both numbers by the smallest prime number possible LCD makes an L LCD = 2 2 2 3 = 24 Ch 8 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Use the Ladder to Find the Least Common Denominator (LCD)!
MULTIPLY numerator and denominator by the same number x 3 x 2 + REWRITE and ADD SIMPLIFY if possible No Can we simplify? (There are no common factors) Ch. 8 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Subtracting a Fraction from a Whole Number
Regrouping PROBLEM: Can we subtract the fraction part as they are? No Why not? We need to regroup the whole number to make a fraction. 5 = 4 + 1 REGROUP REWRITE the problem 5 = 4 + SUBTRACT Ch. 7 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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Let’s Subtract with Renaming!
4 = 3 + 1 4 = 3 + Regrouping 6 PROBLEM: Find common denominators x 2 x 1 - = REGROUP We need to regroup the whole number to make a fraction. REWRITE the problem SUBTRACT and Simplify = 3 = 1 Ch. 9 L 4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5
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