# Instructional Strategies

## Presentation on theme: "Instructional Strategies"— Presentation transcript:

Instructional Strategies

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

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

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

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

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

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

Let's Solve Algebraic Equations

Let's Solve Algebraic Equations

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

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

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

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

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

Let’s Do Long Division! x 6 x 7 x 8 No No Yes  CHECK the 8:

8 6 7 - 150 178 - 175 3 3 Let’s Do Long Division!  FINISH

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

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

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

\$ 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

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

Multiply or Divide from Left to Right

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 42 and multiply 23) 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

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

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

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

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

Step 1 Step 2 Step 3 Let's Solve Equations Undo multiplication

Step 1 Step 2 Step 3 Let's Solve Equations Undo multiplication

Step 1 Step 2 Step 3 Let's Solve Equations Undo Division Simplify

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

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

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

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

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

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

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

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

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

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

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

. Let's Convert Fractions to Decimals ! Now Divide

“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

Let's Convert Decimals to Fractions !

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

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

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

Let’s Add Fractions! 2 6 3 Yes

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

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

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

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

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

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

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

Similar presentations