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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Quarter 1 Instructional Strategies Grade 7 MAP2D

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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) 1.1 Pre-Requisite Skill PROBLEM: Simplify 2 2 – – – –

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Evaluating Algebraic Expressions Section 1.1 Evaluating Algebraic Expressions Evaluate x + 5 for x = Step 1: Step 2: Substitute 11 for x. Add.

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Evaluating Algebraic Expressions Section 1.1 Evaluating Algebraic Expressions Evaluate 2y + 3 for y = 4 11 Step 1: Step 2: Substitute 4 for y. Multiply. Step 3: Add. 2(4)

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Evaluating Algebraic Expressions Section 1.1 Evaluating Algebraic Expressions Evaluate 5x + 2y for x = 13 and y = Step 1: Step 2: Substitute 13 for x and 11 for y. Multiply. Step 3: Add (13) + 2(11)

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Writing Algebraic Expressions Section 1.2 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 multiply product multiplied by of at by divided by quotient every ratio per fraction parts into

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

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

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Absolute value is the distance of a number from zero. The absolute value of -3 is 3. Hint: Count the spaces from zero to the number. The absolute value of 2 is 2. Absolute Value = 32= Section 1.3 Integers & Absolute Value

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

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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. Adding Integers Section 1.4 Adding Integers

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

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

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

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

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Undo addition Step 1 Step 2 Step 3 Check Simplify Solving Equations by Subtracting Section 1.7 Solving Equations by Adding or Subtracting

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Add the opposite Step 1 Step 2 Step 3 Check Simplify Solve Addition Equations Section 1.7 Solving Equations by Adding or Subtracting

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Undo subtraction Step 1 Step 2 Step 3 Check Simplify Solving Equations by Adding Section 1.7 Solving Equations by Adding or Subtracting

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.7 Solving Equations by Adding or Subtracting Undo addition or subtraction Step 1 Step 2 Step 3 Check Simplify Solving Equations by Adding

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Undo multiplication Step 1 Step 2 Step 3 Check Simplify Solving Equations by Dividing Section 1.8 Solving Equations by Multiplying or Dividing

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Solving Equations by Dividing Undo multiplication Step 1 Step 2 Step 3 Check Simplify Section 1.8 Solving Equations by Multiplying or Dividing

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Multiply by the reciprocal Step 1 Step 2 Step 3 Check Simplify Solving Equations by Multiplying Section 1.8 Solving Equations by Multiplying or Dividing

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Solving Equations by Multiplying Undo division Step 1 Step 2 Step 3 Check Simplify Section 1.8 Solving Equations by Multiplying or Dividing

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Section 1.8 Solving Equations by Multiplying or Dividing Undo division Step 1 Step 2 Step 3 Check Simplify Rewrite Solving Equations by Multiplying

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Solving Two-Step Equations Section 1.9 Solving Two- Step Equations Step 1 6x – 2 = x = x = 2 Step 2 Add 2 to both sides of the equation Then divide both sides by 6 Step 3 Simplify

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Solving Two-Step Equations Section 1.9 Solving Two- Step Equations Step 1 -5 x = 48 Step 2 Subtract 5 from both sides of the equation Then multiply both sides by 6 Step 3 Simplify -5

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

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

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

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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 CHECK to see the answer is close to the estimate 5.75 is close to 6 0 SUBTRACT Section 2.3 Adding and Subtracting Rational Numbers

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

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

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

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

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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 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 Section 2.4 Multiplying Rational Numbers

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

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Divide Decimals PROBLEM: = 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 Section 2.5 Dividing Rational Numbers

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

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Add Fractions MULTIPLY denominators to find a 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 Section 2.6 Adding & Subtracting with Unlike Denominators

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

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

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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Subtracting Mixed Numbers with Regrouping Can we subtract the fraction parts as they are? REGROUP PROBLEM: Why not?2 is bigger than 1 REWRITE the problem SUBTRACT 3 5 = = = 4 REGROUPING

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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. DRAW THE L SHAPE DIVIDE out common prime numbers starting with the smallest LCM makes an L: LCM = = 72 GCF = = = 3 2 GCF is down the left side: Simplified fraction is on the bottom

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

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

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