Instructional Strategies Grade 7 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Writing Algebraic Expressions Word Wall, Graphic Organizer or Foldable + - add sum plus more than all together total gain rose subtract minus difference loss of take away drop fewer than* less than* = equals is divided by quotient every ratio per fraction parts into multiply product multiplied by of at by × ÷ Section 1.2 Writing Algebraic Expressions Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Section 1.3 Integers & Absolute Value -3 -2 -1 1 2 3 4 5 All whole numbers and their opposites Zero is not positive or negative Section 1.3 Integers & Absolute Value Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Opposite numbers are the same Opposites 4 -4 -3 3 -2 2 -1 1 Opposite numbers are the same distance from zero. The opposite of -2 is 2. The sum of opposites is 0. Section 1.3 Integers & Absolute Value Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Absolute Value Absolute value is the distance of a number from zero. The absolute value of -3 is 3. -3 = 3 -1 1 -2 2 -3 3 4 5 6 The absolute value of 2 is 2. 2 = 2 -1 1 -2 2 -3 3 4 5 6 Hint: Count the spaces from zero to the number. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.3 Integers & Absolute Value

Adding Integers -3 3 -2 2 -1 1 4 5 6 Same Signs, Add 4 5 6 Same Signs, Add Keep the same sign. Different Signs, Subtract Keep the sign of the number with the largest absolute value. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.4 Adding Integers

Adding Integers If both integers are +, the sum is positive If both integers are -, the sum is negative If integers have different signs. Subtract the numbers. Note: The sign of the number with the largest absolute value determines the sign that goes with the answer. Section 1.4 Adding Integers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Adding Integers 2 + -3 = -1 2 + 3 = 5 -2 + 3 = 1 -2 + -3 = -5 If the signs are different, subtract. If the signs are the same, add. 2 + -3 = -1 2 + 3 = 5 -2 + 3 = 1 -2 + -3 = -5 The sign of the number with the largest absolute value determines the sign of the answer. Section 1.4 Adding Integers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Subtracting Integers Subtraction is defined as adding the opposite of the number. Rewrite subtraction as an addition expression. Different Signs Keep the sign of the +3 Use Addition Rules. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.5 Subtracting Integers

Subtracting Integers Subtraction is defined as adding the opposite of the number. Rewrite subtraction as an addition expression. Different Signs Keep the sign of the 4 Use Addition Rules. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.5 Subtracting Integers

Multiplying and Dividing Integers Same Signs - POSITIVE Different Signs - NEGATIVE -9  -5 = 45 -9  5 = -45 Two negatives - One negative MAKE A POSITIVE STAYS NEGATIVE Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.6 Multiplying Integers & Dividing Integers

Compare Fractions COMMON DENOMINATORS If the denominators are the same, compare numerators. COMMON NUMERATORS If the numerators are the same, compare denominators. (Big denominators make small fractions.) Section 2.2 Ordering Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

SHORTCUT: Skip step 1, multiply diagonally and compare. Compare Fractions UNLIKE DENOMINATORS Find a common denominator by multiplying the denominators. 15 16 < x Find the numerators by multiplying diagonally upwards. Compare the new numerators. SHORTCUT: Skip step 1, multiply diagonally and compare. Section 2.2 Ordering Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Add Decimals PROBLEM: 12.34 + 5.6 =  ESTIMATE as 12 + 6 = 18  REWRITE the expression vertically, line up decimals  FILL IN the empty spaces with zeros 17.94 is close to 18   PLACE the decimal point in the sum  ADD  CHECK to see the answer is close to the estimate Section 2.3 Adding and Subtracting Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Subtract Decimals PROBLEM: 8.95 – 3.2 =  ESTIMATE as 9 – 3 = 6  REWRITE the expression vertically, line up decimals  FILL IN the empty spaces with zeros  PLACE the decimal point in the difference 5.75 is close to 6   SUBTRACT  CHECK to see the answer is close to the estimate Section 2.3 Adding and Subtracting Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Add Fractions 3 3 2 6 2 3 Yes When the denominators are the same, add the numerators 3 3 2 6 2 3 Can we simplify? Yes Use prime factors Section 2.3 Adding & Subtracting Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

The Matching Factors Method Multiply Fractions The Matching Factors Method PROBLEM:  REWRITE the expression  FACTOR composite numbers  DIVIDE OUT common factors (CANCEL) 2 4 3 3  MULTIPLY any remaining factors 2 2 Section 2.4 Multiplying Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

1 1 3 4 Multiply Fractions PROBLEM:  REWRITE the expression The Canceling Method PROBLEM:  REWRITE the expression  Look for numbers with common factors in the numerator & denominator 1 1 2 goes into both 2 and 8 2 into 2 is? 2 into 8 is? 3 4 3 goes into both 3 and 9 3 into 3 is?  DIVIDE OUT common factors (CANCEL) 3 into 9 is? Section 2.4 Multiplying Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

1 1 3 4 Multiply Fractions PROBLEM:  REWRITE the expression Section 2.4 Multiplying Rational Numbers The Canceling Method PROBLEM:  REWRITE the expression  Look for numbers with common factors in the numerator & denominator 1 1 3 4  DIVIDE OUT common factors (CANCEL)  MULTIPLY any remaining factors Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Multiply Decimals PROBLEM: 12.3 x 4.5 =  ESTIMATE as 12 x 5 = 60 Section 2.4 Multiplying Rational Numbers 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 55.35 is close to 60   CHECK to see the answer is close to the estimate Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

2 10 2 5 Divide Fractions  PROBLEM:    CIRCLE the  and the divisor   REWRITE as multiplication by the reciprocal   REVERSE everything in the circle! 2 10 2 5  MULTIPLY Section 2.5 Dividing Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

5 6 40 4 8 4 8 Divide Decimals PROBLEM: 4.48  0.08 =  REWRITE 0.08 into 4.48 40  MOVE decimals 2 places right by multiplying divisor and dividend by 100 4 8 4 8  DIVIDE  PLACE the decimal point in the quotient Section 2.5 Dividing Rational Numbers Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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. Section 2.6 Adding & Subtracting with Unlike Denominators Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Add Fractions No  MULTIPLY denominators to find a common denominator Section 2.6 Adding & Subtracting with Unlike Denominators PROBLEM:  MULTIPLY denominators to find a common denominator x 3 x 2 x 3 x 2  Multiply numerator and denominator by the same number  REWRITE and ADD  SIMPLIFY if possible No Can we simplify? 5 and 6 are consecutive Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Add Fractions 18 + 8 48 Here is a shortcut: Multiply along the arrows Simplify Section 2.6 Adding & Subtracting with Unlike Denominators Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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 HAVE a fraction. 5 = 4 + 1  REGROUP 4  REWRITE the problem 5 = 4 + 4  SUBTRACT Section 2.6 Adding & Subtracting with Unlike Denominators Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Subtracting Mixed Numbers with Regrouping  PROBLEM:  Can we subtract the fraction parts as they are? No Why not? 2 is bigger than 1  5 = 4 + 1 +  REGROUP  REWRITE the problem 5 = 4 + +  3 5 = 4  SUBTRACT Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Use the Ladder for LCM, GCF and Simplifying Fractions  WRITE the two numbers on one line. 2 24 36 2 12 18  DRAW THE L SHAPE  DIVIDE out common prime numbers starting with the smallest 3 6 9 2 3  LCM makes an L: LCM = 2  2  3  2  3 = 72 GCF is down the left side: GCF = 2  2  3 = 12 36 24 = 3 2 Simplified fraction is on the bottom Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Convert Improper Fractions to Mixed Numbers 2 1 5 3 = = 5 3 3 3 1 2 1 Improper Fraction Mixed Number Divide Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

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 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 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7