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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 1 MAP 2 D Trimester 1 Instructional Strategies Grade 5 Updated 6/10.

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Presentation on theme: "Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 1 MAP 2 D Trimester 1 Instructional Strategies Grade 5 Updated 6/10."— Presentation transcript:

1 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 1 MAP 2 D Trimester 1 Instructional Strategies Grade 5 Updated 6/10

2 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 2 Let’s Round Numbers! Long Beach Unified School District has 96, 572 students enrolled. Round this to the nearest __________.  Underline the word that comes after “nearest”.  Underline the digit in the indicated place.  If the circled digit is 5 or greater, add one to the underlined place and change all digits to the right to zeros.  Circle the digit to the right of the underlined place.  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

3 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 3 Let’s Round Numbers! Example: What is 45,638 rounded to the nearest thousand? 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 Ch 1 L 3 45,500 4 or less, stays the same 5 or higher, add one more

4 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 4 Let’s Round Numbers ! thousands tens ones tenths hundredths thousandths hundreds Ch 2.1 & Ch 11.1 Example: What is rounded to the nearest hundredths? Two hundred fifty-seven AND forty-four hundredths

5 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 5 Let’s Add Decimals! PROBLEM: =  ESTIMATE as = 18  REWRITE the expression vertically, line up by place value and decimals  FILL IN the empty spaces with zeros  PLACE the decimal point in the sum is close to  ADD Ch & 2.1 tens ones tenths hundredths CHECK to see the answer is close to the estimate

6 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 6 Let’s Subtract Decimals! PROBLEM: 8.95 – 3.2 =  ESTIMATE as 9 – 3 = 6  REWRITE the expression vertically, line up by place value and decimals  FILL IN the empty spaces with zeros  PLACE the decimal point in the difference 5.75 is close to 6 0  SUBTRACT Ch & 2.1 CHECK to see the answer is close to the estimate ones tenths hundredths

7 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 7 Equal Decimals!  Which decimal is greater?  READ THEM CORRECTLY like reading fractions  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 or is equal to  0 Ch. 11 L 2

8 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 8 Use inverse operation to find the missing variable. Ch. 14 L 4

9 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 9 Use inverse operation to find the missing variable. Ch. 14 L 4

10 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 10 Use inverse operation to find the missing variable. Ch. 14 L 4

11 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 11 Why the Zero Place Holder?  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. PROBLEM: 23 X 45   0 It’s All About the Facts

12 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 12 Let’s Multiply Decimals! PROBLEM: 12.3 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  CHECK to see the answer is close to the estimate is close to 60 Ch. 12 L 5

13 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 13 Let’s Multiply Decimals with ZEROS in the Product! PROBLEM: 0.17 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  PLACE the decimal in front of the last digit that was underlined  CHECK to see the answer is close to the estimate is close to 0 00 Ch. 12 L 5

14 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 14 Let’s Do Long Division!  Does the 2-digit divisor go into the 1 st two digits of the dividend? (Does 25 go into 16?)  UNCOVER the next digit in the dividend. (Does 25 go into 167?) How many times does 25 go into 1678? No idea… Let’s use a shorter problem! Ch. 4 L 5

15 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 15 Let’s Do Long Division!  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. x 8 Ch. 4 L 5

16 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 16 Let’s Do Long Division!  CHECK the 8:  TRY AGAIN: x 8  TRY AGAIN: x 7 x 6 Ch. 4 L 5

17 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 17 Let’s Do Long Division!  FINISH R3  Look back at your work to help you solve the problem! Ch. 4 L 5

18 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 18 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? There will be 3 full boxes. Another box is needed for the 4 extra puppets. So 4 boxes are needed in all. Ch 13 L 3 R4

19 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 19 Let’s Solve Division Problems When you solve a division problem, you can 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? Sometimes you write the remainder as a FRACTION. Each frame required 3 feet of framing material. Ch 13 L 3 -

20 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 20 Let’s Solve Division Problems When you solve a division problem, you can write the remainder as a decimal. Ch. 13 L x PROBLEM: =  REWRITE 12 into 366  DIVIDE like regular whole numbers  If there is a remainder, place a decimal and a zero in the dividend  Bring up the decimal in the quotient and continue to divide 0

21 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 21 Let’s Divide Money PROBLEM: $9.80  4 =  REWRITE 4 into $9.80  WRITE the dollar sign and decimal in the quotient  DIVIDE 0 $ Ch. 13 L 3

22 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 22 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

23 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 23 Parentheses Multiply or Divide from Left to Right Exponents Add or Subtract from Left to Right Ch. 14 L 2

24 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 24 P Parentheses MD Multiply or Divide from Left to Right E Exponents AS Add or Subtract from Left to Right Order of Operations (there are none here) (perform 2 squared first) (divide 4  2 and multiply 2  3) (subtract 4-2, then add 6) PROBLEM: Simplify 2 2 – 4   – 4   3 4 – 4   – Ch 14 L 2

25 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 25 Parentheses First Add or Subtract from Left to Right Multiplication or Division from Left to Right Ch. 14 L 2 60 – 3 x (10 + 8) 60 – 3 x

26 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 26 Ch. 14 L 2 Parentheses First Substitute for the variable Multiplication or Division from Left to Right (No Addition or Subtraction) 4 x ( p + 15) 4 x 20 4 x (5 + 15) 80 p = 5

27 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 27 Ch. 14 L 2 m = 6 (10 + m) 4 Substitute for the variable Parentheses First Multiplication or Division from Left to Right (No Addition or Subtraction) (10 + 6)

28 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 28 Ch. 14 L 2 n = n Substitute for the variable (No Parentheses) Multiplication or Division from Left to Right Add or Subtract from Left to Right

29 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 29 Ch 14 L 4 Undo multiplication Step 1 Step 2 Step 3 Check Simplify

30 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 30 Ch 14 L 4 Undo multiplication Step 1 Step 2 Step 3 Check Simplify

31 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 31 Ch 14 L 4 Undo Division Step 1 Step 2 Step 3 Check Simplify

32 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 32 The Distributive Property Four is multiplying the quantity “x + 3” That means four will multiply both the x and the 3!  Multiply 4 times x PROBLEM: 4(x + 3)  Copy the operation sign  Multiply 4 times 3 Ch. 14 L 5 4(x + 3) 4 times x4 times 3 4x4x + 12

33 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 33 Use Distributive Property to Find the Missing Variable Problem: 5 x 36 = (5 x 30) + (5 x n) Cross out matching numbers on both sides of the equal sign Circle what is left 6 x 25 = (6 x m) + (6 x 5) m = 20 5 x 36 = (5 x 30) + (5 x n) Problem: 6 x 25 = (6 x m) + (6 x 5) n = Ch 15 L 5

34 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 34 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) p = 60 Ch 15 L 5

35 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 35 Prime Numbers  What are the first seven prime numbers? 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. 2, 3, 5, 7, 11, 13, 17 Ch. 5 L 1 & 5

36 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 36 Let’s Factor and Use Exponents!  What are 2 factors with a product of 56? Circle the PRIME FACTORS and…  Continue to factor any COMPOSITE NUMBERS. 56 PROBLEM: Write the prime factorization of 56.  Continue until only prime numbers remain.  Write prime factorization in exponential form = 2 37 Ch. 5 L 5

37 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 37 Hint: Little goes after big! x 6 18 x 5 5 Think: “4 times what equals 24?” Since 4 x 6 = 24, we will also multiply the numerator by 6. Think: “3 times what equals 15?” Since 3 x 5 = 15, then “5 times what equals 25?” So 5 is the missing number. Ch 6 L 1

38 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 38 Let’s Simplify Fractions! 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 Ch. 6 L x

39 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 39 Tips for Recognizing Simplified Fractions  When the numerator and denominator are CONSECUTIVE numbers the fraction is in simplest form.  When the denominator is PRIME the fraction is in simplest form. and many more! MAP 2 D

40 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 40 Tips for When to Simplify a Fraction  You must simplify a fraction if both numbers are EVEN.  You must simplify a fraction if the denominator is DIVISIBLE by the numerator. and many more! MAP 2 D

41 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 41 Let’s Convert Mixed Numbers to Improper Fractions! How many thirds are in the whole number? FIRST multiply denominator by the whole number 3 x 4 NEXT PLUS how many thirds are in the fraction? 3 x 4 = 12 3 Keep the same denominator LAST The sum is the numerator = add the product to the numerator Ch 6 L 3

42 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade Improper Fraction Divide Mixed Number Let’s Convert Improper Fractions to Mixed Numbers! = = Section 3-4 Ch 6 L 3

43 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 43 First, add a decimal and write 2 zeros. Next, put a decimal in the quotient.. Ch. 6 L 6 Now Divide

44 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade Ch. 6 L 6 = 0.25 “One fourth is equal to twenty-five hundredths” OR “One quarter is worth twenty-five cents” Fraction Decimal

45 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 45 Ch. 6 L 6 1.Write the decimal as a fraction. 2.Simplify the fraction using prime factorization

46 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 46 Four and twenty-five hundredths Ch. 6 L hundreds tens ones Decimal point tenths hundredths = 4 (OR 4 )

47 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 47  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. Ch.6 L 7 Let’s Find Point A on the Number Line: Point A is located at

48 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 48 Example: What number does Point T represent on the number line? Point T is located at Ch.6 L 7

49 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 49 Let’s Add Fractions! Can we simplify? Use prime factors When the denominators are the same, add the numerators: Ch. 7 L

50 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 50 Let’s Add Fractions!  Can we add these as they are?  First ask if one denominator goes into the other. PROBLEM: Why not?They have unlike denominators. TO FIND A COMMON DENOMINATOR: Does 3 go into 12 evenly? We will use 12 as the common denominator. Ch. 8.4 & 8.5

51 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 51 Let’s Add Fractions!  Multiply numerator and denominator by the same number Can we simplify?  SIMPLIFY if possible  REWRITE and ADD Ch. 8.4 & 8.5 x 1 x 4 x 1 + x

52 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 52 Let’s Add Fractions!  Multiply denominators to find common denominator  Multiply numerator and denominator by the same number Can we simplify? 5 and 6 are consecutive  SIMPLIFY if possible PROBLEM: x 3x 3 x 3x 3 x 2x 2 x 2x 2  REWRITE and ADD Ch. 8.4 & 8.5

53 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 53 Let’s Use the Ladder to Find the Least Common Denominator (LCD)!  WRITE the two denominators on one line  Draw a step in the shape of an “L”  DIVIDE both numbers by the smallest prime number possible  LCD makes an L LCD = 2  2  2  3 = 24 Ch 8 L 4 Example:

54 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 54 Let’s Use the Ladder to Find the Least Common Denominator (LCD)!  MULTIPLY numerator and denominator by the same number Can we simplify? (There are no common factors)  SIMPLIFY if possible  REWRITE and ADD Ch. 8 L 4 x 3x 3 x 3x 3 x 2x 2 x 2x 2 +

55 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 55 Subtracting a Fraction from a Whole Number  Can we subtract the fraction part as they are?  REGROUP PROBLEM: Why not? We need to regroup the whole number to make a fraction.  REWRITE the problem  SUBTRACT 5 = = 4 + Regrouping Ch. 7 L 4

56 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 5 56 Let’s Subtract with Renaming!  Find common denominators  REGROUP PROBLEM: We need to regroup the whole number to make a fraction.  REWRITE the problem  SUBTRACT and Simplify Ch. 9 L 4 x 2 x 1 x 2 - x 1 = = = 3 4 = = 3 +  Regrouping 6 6


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