copyright ©, long beach unified school district. all rights reserved. - grade 7 quarter 1...

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

Quarter 1Instructional Strategies

Grade 7

MAP2D


PParentheses

MMultiply or DDivide from Left to Right

EExponents

AAdd or SSubtract from Left to Right

Order of Operations

(there are none here)

(perform 2 squared first)

(divide 42 and multiply 23)

(subtract 4-2, then add 6)1.1 Pre-Requisite Skill

PROBLEM: Simplify 22 – 4 2 + 2 3

22 – 4 2 + 2 3

4 – 4 2 + 2 3

4 – 2 + 6 2 +

68


Evaluating Algebraic Expressions

Section 1.1 Evaluating Algebraic Expressions

Evaluate x + 5 for x = 11

11 + 5

16

Step 1:

Step 2:

Substitute 11 for x.

Add.




Evaluate 2y + 3 for y = 4

11

Step 1:

Step 2:

Substitute 4 for y.

Multiply.

Step 3: Add.

2(4) + 3

8 + 3




Evaluate 5x + 2y for x = 13 and y = 11

11

Step 1:

Step 2:

Substitute 13 for x and 11 for y.

Multiply.

Step 3: Add.

65 + 22

5(13) + 2(11)


Writing Algebraic Expressions

Section 1.2 Writing Algebraic Expressions

Word Wall, Graphic Organizer or Foldableadd sum

plus more thanall togethertotal gainrose

+ -

× ÷

=

subtract minusdifference loss of take away drop fewer than*

less than*equals ismultiplyproductmultiplied byof at by

divided by quotientevery ratioper fractionparts into


-3 -2 -1 0 1 2 3 4 5 All whole numbers and their opposites

Zero is not positive or negative

33 Section 1.3 Integers & Absolute Value

Integers


0 -1 1 -2 2 -3 3

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


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

0 -1 1 -2 2 -3 3 4 5 6

-3 = 3

2 = 2

0 -1 1 -2 2 -3 3 4 5 6

Section 1.3 Integers & Absolute Value


213

413 413

213

Same Signs, Add

Different Signs, Subtract

Keep the same sign.

Keep the sign of the number with the largest absolute value.

Adding Integers

0 -1 1 -2 2 -3 3 4 5 6

Section 1.4 Adding Integers


15510

15510

5510 5510

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 thenumber with the largest absolute value determines the sign that goes with the answer.

Adding Integers



If the signs are the same, add.

The sign of thenumber with the largest

absolute value determines the sign of the answer.

Adding IntegersIf the signs are

different, subtract.

-2 + -3

2 + 3 = 5

= -5 -2 + 3

2 + -3 = -1

= 1



13

Subtraction is defined as adding the opposite of the number.

13 Rewrite subtraction as an addition expression.

Use Addition Rules.

213 Different Signs

Keep the sign of the +3

Subtracting Integers

Section 1.5 Subtracting Integers


42

Subtraction is defined as adding the opposite of the number.

42 Rewrite subtraction as an addition expression.

Use Addition Rules.

242

Different Signs Keep the sign of the 4

Subtracting Integers

Section 1.5 Subtracting Integers


Multiplying and Dividing Integers

STAYS NEGATIVEOne negative

Different Signs - NEGATIVE

98

72

-9 5 = -45

MAKE A POSITIVETwo negatives -

Same Signs - POSITIVE

9872

-9 -5 =

45

Section 1.6 Multiplying Integers & Dividing Integers


146x

80 x66

8x

Undo addition

1468

Step 1

Step 2

Step 3 Check

Simplify

Solving Equations by Subtracting

Section 1.7 Solving Equations by Adding or Subtracting


146 x

200 x66

20x

Add the opposite

14206

Step 1

Step 2

Step 3 Check

Simplify

Solve Addition Equations



146x

200 x

66

20x

Undo subtraction

14620

Step 1

Step 2

Step 3 Check

Simplify

Solving Equations by Adding



1923 n


n 19023nn

Undo addition or subtraction

19423

Step 1

Step 2

Step 3 Check

Simplify1919 n1923

n4

Solving Equations by Adding


427 k

742

77 k

61 k

Undo multiplication

4267

Step 1

Step 2

Step 3Check

Simplify

6k

Solving Equations by Dividing

Section 1.8 Solving Equations by Multiplying or Dividing


n945

99

945 n

n5

5945

n15

Solving Equations by Dividing

Undo multiplication

Step 1

Step 2

Step 3Check

Simplify



2052 k

501 k

Multiply by the reciprocal

20 5052

Step 1

Step 2

Step 3Check

Simplify50 k

Solving Equations by Multiplying

25

2052

25

k



59

c

959

9 c

45c

5945

451 c


Undo division

Step 1

Step 2

Step 3Check

Simplify



59c


959

9 c

45c

Undo division

5945

Step 1

Step 2

Step 3

Check

Simplify

59c

Rewrite

451 c



Solving Two-Step Equations

Section 1.9 Solving Two-Step Equations

Step 1 6x – 2 = 10

+ 26x = 12

+ 2

2 2x = 2

Step 2

Add 2 to both sides of the equation

Then divide both sides by 6

Step 3Simplify


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 3Simplify

136

5 x

-5

6)8()6

(6 x


Compare Fractions

If the denominators are the same, compare numerators.

If the numerators are the same, compare denominators. (Big denominators make small fractions.)

85

83

21

61

COMMON DENOMINATORS

COMMON NUMERATORS

Section 2.2 Ordering Rational Numbers


x

Compare Fractions

Find a common denominator by multiplying the denominators.

Find the numerators by multiplying diagonally upwards.

54

43

UNLIKE DENOMINATORS

Compare the new numerators.

20

201615 <

SHORTCUT: Skip step 1, multiply diagonally and compare.

Section 2.2 Ordering Rational Numbers


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 PLACE the decimal point in

the sum

CHECK to see the answer is close to the estimate

4971

65

4321

.

.

.

17.94 is close to 18

0 0

ADD

Section 2.3 Adding and Subtracting Rational

Numbers


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


575

23

598

.

.

.

5.75 is close to 6

0

SUBTRACT

Section 2.3 Adding and Subtracting Rational

Numbers


Add Fractions

Can we simplify?

128

121

129

43

2 6

3 3

2 3Use prime factors

When the denominators are the same, add the numerators

Section 2.3 Adding & Subtracting Rational

Numbers


Multiply Fractions

PROBLEM:

REWRITE the expression

FACTOR composite numbers

83

92

3 3 DIVIDE OUT common

factors (CANCEL)

8932

121

2223332

2 4

2 2 MULTIPLY any

remaining factors

The Matching Factors Method

Section 2.4 Multiplying

Rational Numbers


Multiply Fractions

PROBLEM:


Look for numbers with common factors in the numerator & denominator

83

92

DIVIDE OUT common factors (CANCEL)

8932

The Canceling Method

2 goes into both 2 and 8

3 goes into both 3 and 9

1 1

3 4

2 into 2 is?2 into 8 is?

3 into 3 is?3 into 9 is? Section 2.4

Multiplying Rational Numbers


Multiply Fractions

PROBLEM:


Look for numbers with common factors in the numerator & denominator

83

92

DIVIDE OUT common factors (CANCEL)

8932

121

MULTIPLY any remaining factors

The Canceling Method

1 1

3 4

Section 2.4 Multiplying Rational

Numbers


Multiply DecimalsPROBLEM: 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


5355

0294

516

54

321

.

.

55.35 is close to 60

Section 2.4 Multiplying Rational

Numbers


52253

Divide Fractions

PROBLEM:

CIRCLE the and the divisor

REWRITE as multiplication by the reciprocal

51

203

REVERSE everything in the circle!

MULTIPLY

2053

2 10

2 5

43

51

203

15

203

Section 2.5 Dividing Rational Numbers


48.408.0

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

5

4048

6

4 8

0

Section 2.5 Dividing Rational Numbers


Add Fractions

32

121

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?

32

121

We will use 12 as the common denominator.Section 2.6 Adding &

Subtracting with Unlike Denominators


Add Fractions

MULTIPLY denominators to find a common denominator Multiply numerator

and denominator by the same number

31

21

Can we simplify? 5 and 6 are consecutive

SIMPLIFY if possible

31

21

PROBLEM

:

x 3

x 3

x 2

x 2

REWRITE and ADD 62

63

65

Section 2.6 Adding & Subtracting with

Unlike Denominators


Add Fractions

61

83

Here is a shortcut:

4818+8

4826

2413

Multiply along the arrows

AddSimplify

Section 2.6 Adding & Subtracting with Unlike

Denominators


32

5

Subtracting a Fraction from a Whole Number

32

5

Can we subtract the fraction part as they are?

REGROUP

PROBLEM:

Why not?

We need to regroup the whole number to HAVE a fraction.

32

5

REWRITE the problem

SUBTRACT

5 = 4 + 1

5 = 4 +33

32

33

4

Regrouping

4

31

4 Section 2.6 Adding & Subtracting with Unlike

Denominators


Subtracting Mixed Numbers with Regrouping

32

131

5

Can we subtract the fraction parts as they are?

REGROUP

PROBLEM:

Why not? 2 is bigger than 1

32

131

5

REWRITE the problem

SUBTRACT

32

134

4

32

3

5 = 4 + 1 +

31

31

5 = 4 + +

31

31

33

5 = 431

34

REGROUPING


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

242 36122 18

63 92 3

LCM makes an L: LCM = 2 2 3 2 3 = 72

GCF = 2 2 3 = 12

3624

=32

GCF is down the left side:

Simplified fraction is on the bottom


35

32

153

Improper Fraction Divide

Mixed Number

53

1

32

23

Convert Improper Fractions to Mixed Numbers

= =


Convert Mixed Numbers to Improper Fractions

How many thirds are in the whole number?

32

4FIRST multiply denominator by the whole number

3 x 4

NEXT

PLUS how many thirds are in the fraction?

3 x 4 = 12

3Keep the same denominator

LAST The sum is the numerator

32

4

12 + 2

12 + 2 = 1414

add the productto the numerator

copyright ©, long beach unified school district. all rights reserved. - grade 7 quarter 1...

Documents

integers absolute value

subtracting integers

multiplying integers

dividing integers

opposite step

negative section

map2d slide

addition equations section