MAP 2 D

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

MAP2D

Quarter 1Instructional Strategies

Grade 6


MAP2D

Chapter 1Algebraic Reasoning

Chapter 2Integers

Part of Chapter 3Number Theory andFractions (3.1-3.3)


MAP2D

Instructional Strategies

Chapter 1Algebraic Reasoning


Exponents

SDAP 1.1 Mean, Median, Mode, and Range 7.1

•Multiplication can be written as a power

•There is a base and an exponent

•The exponent tells how many times to use the base as a factor

= =base

exponent

= =

This is read as, “5 to the

second power” or “5

squared.”


322422

Parentheses

Multiply or Divide from Left to RightExponents

Add or Subtract from Left to Right

Ch. 14 L 2


Order of Operations

Exponents

Parentheses

Multiplication Division

SubtractionAdditionin order from left to right

in order from left to right

or

or


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)

PROBLEM: Simplify 22 – 4 2 + 2 3

22 – 4 2 + 2 3

4 – 4 2 + 2 3

4 – 2 + 6 2 +

68


Commutative Properties

Think of “commuting” from home to school…

Addition 4 + 5 = 5 + 4 a + b = b + a

Addends trade places

3 + (7 + 6) = (7 + 6) + 3

Multiplication3 ∙ 6 = 6 ∙ 3 ab = ba

Factors trade places

5(4 ∙ 8) = (4 ∙ 8)5

It’s like what you learned in All About the Facts!

Properties


Associative Properties

Groups change, Numbers stay in same order

Addition (7 + 5) + 6 = 7 + (5 + 6)

a + (b + c) = (a + b) + c

You are just regrouping the numbers so “friends” can be together.

Multiplication 4(3 ∙ 7) = (4 ∙ 3)7

(a ∙ b)c = a(b ∙ c)


Distributive Property

Think of a teacher distributing something to every student in the class.

cabacba )( cabacba )(and


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

4(x + 3)

4 times x 4 times 3

4x + 12

Ch. 3 Section # 1


Identity PropertyThe sum of 0 and any

number is the number. The product of 1 and

any number is the number

33x

1=

5 + 0=5Whenever you add zero and

multiply by 1, the answer will ALWAYS be the original

number.

It’s like looking in a mirror!


Writing Algebraic ExpressionsWord 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


146x

80 x66

8x

Undo addition

1468

Step 1

Step 2

Step 3 Check

Simplify

Solving Equations by 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


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



MAP2D


Chapter 2Integers


Adding Integers Song!Adding Integers

(to the tune of Row, Row, Row Your Boat)

Same Signs Add and Keep,

Different Signs Subtract,

Take the Sign of the Higher Number,

Then it’ll be Exact!

Ch 15 L 4


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

Zero is not positive or negative

33

Integers


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


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


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


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


Multiplying and Dividing Integers

+

--

Cover up the signs that are being multiplied or divided

-9 -5 = 45In the example, since 9 is

negative and so is 5, with two fingers cover the two negative signs

Since, the sign that isn’t covered is POSITIVE, the answer is POSITIVE 45

-9 2 = -18 36÷(-4)=-9

Try these: 98

72


Solving Equations Containing Integers

Which operation needs to be undone?

Solve for X.

Undo the subtraction, by doing the inverse operation of adding. Remember to undo both sides.

Cancel out. Don’t forget the integer rules.


Solving Equations Containing Integers

Which operation needs to be undone?

Solve for X.

Undo the division, by doing the inverse operation of multiplication. Remember to undo both sides.

Cancel out. Don’t forget to show all of your work.


MAP2D


Part of Chapter 3Number Theoryand Fractions

(3.1-3.3)


Prime Numbers

What are the first seven prime numbers?

② 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


Let’s Factor and Use Exponents!

What are 2 factors with a product of 56?

② 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.

7 8

2 4

2 2

56 = 23•7


Let’s 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


Let’s Use the Ladder for LCM and GCD with 3 or more numbers

WRITE the two numbers on one line. DRAW THE L SHAPE

DIVIDE out common prime numbers (at least 2 must be in common)

42 1233 612 2

1 1

LCM makes an L:LCM = 2 3 2 1 1 1 = 12

GCF = 2GCF* is down the left side:

62

*Numbers that can not be divided out, CIRCLE and bring STRAIGHT down

21

*If a number is circled, cross out the divisor that corresponds, and do not use it to find the GCD.

xx


GCD vs LCM: Problem Solving

• Are things being split into smaller sections?

• How many people can we invite?

• Are we arranging into rows or groups?

• Do we have to purchase multiple items?

• Are we trying to figure how soon an event will happen at the same time?

GCD LCM

MAP 2 D

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