Instructional Strategies MAP2D Quarter 1 Instructional Strategies Grade 6

MAP2D Chapter 1 Algebraic Reasoning Chapter 2 Integers Part of Chapter 3 Number Theory and Fractions (3.1-3.3)

Instructional Strategies Chapter 1 Algebraic Reasoning MAP2D Instructional Strategies Chapter 1 Algebraic Reasoning

Exponents 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 exponent 4 2 = = 2 2 2 2 16 This is read as, “5 to the second power” or “5 squared.” base 2 5 = = 25 5 5 SDAP 1.1 Mean, Median, Mode, and Range 7.1 2 2 2

Multiply or Divide from Left to Right Order of Operations Parentheses Exponents Multiply or Divide from Left to Right Add or Subtract from Left to Right Ch. 14 L 2

Order of Operations Parentheses Exponents Multiplication Division in order from left to right Addition Subtraction or in order from left to right

PROBLEM: Simplify 22 – 4 2 + 2  3 Order of Operations PROBLEM: Simplify 22 – 4 2 + 2  3 Parentheses 22 – 4  2 + 2  3 (there are none here) Exponents 4 – 4  2 + 2  3 (perform 2 squared first) 4 – 2 + 6 Multiply or Divide from Left to Right 2 + 6 (divide 42 and multiply 23) Add or Subtract from Left to Right 8 (subtract 4-2, then add 6)

Properties Commutative Properties Addition 4 + 5 = 5 + 4 a + b = b + a It’s like what you learned in All About the Facts! Properties 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 Multiplication 3 ∙ 6 = 6 ∙ 3 ab = ba Factors trade places 5(4 ∙ 8) = (4 ∙ 8)5

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 and + 5 5 = + Think of a teacher distributing something to every student in the class.

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  Multiply 4 times x 4(x + 3)  Copy the operation sign 4x + 12  Multiply 4 times 3 Ch. 3 Section # 1

It’s like looking in a mirror! Identity Property The sum of 0 and any number is the number. The product of 1 and any number is the number 3 x 1= 3 Whenever you add zero and multiply by 1, the answer will ALWAYS be the original number. It’s like looking in a mirror! 5 + 0= 5

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 × ÷

Solving Equations by Subtracting Step 1 Undo addition Step 2 Simplify Step 3 Check

Solve Addition Equations Step 1 Add the opposite Step 2 Simplify Step 3 Check

Solving Equations by Adding Step 1 Undo subtraction Step 2 Simplify Step 3 Check

Solving Equations by Adding Undo addition or subtraction Step 1 Step 2 Simplify Step 3 Check

Solving Equations by Dividing Step 1 Undo multiplication Step 2 Simplify Step 3 Check

Solving Equations by Dividing Step 1 Undo multiplication Step 2 Simplify Step 3 Check

Solving Equations by Multiplying Step 1 Multiply by the reciprocal Step 2 Simplify Step 3 Check

Solving Equations by Multiplying Step 1 Undo division Step 2 Simplify Step 3 Check

Solving Equations by Multiplying Rewrite Step 1 Undo division Step 2 Simplify Step 3 Check

Instructional Strategies Chapter 2 Integers MAP2D Instructional Strategies Chapter 2 Integers

Adding Integers Song! Same Signs Add and Keep, (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

Integers -3 -2 -1 1 2 3 4 5 All whole numbers and their opposites 1 2 3 4 5 All whole numbers and their opposites Zero is not positive or negative

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.

If integers have different signs. Subtract the numbers. 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.

Adding Integers 2 + -3 = -1 2 + 3 = 5 -2 + 3 = 1 -2 + -3 = -5 If the signs are the same, add. If the signs are different, subtract. 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.

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.

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.

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

Multiplying and Dividing Integers +  Cover up the signs that are being multiplied or divided -9  -5 = 45  In 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  Try these: -9  2 = -18 36÷(-4)=-9

Solving Equations Containing Integers     Which operation needs to be undone?     Undo the subtraction, by doing the inverse operation of adding. Remember to undo both sides.         Cancel out. Don’t forget the integer rules.         Solve for X.

Solving Equations Containing Integers     Which operation needs to be undone?         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.           Solve for X.

Instructional Strategies Part of Chapter 3 MAP2D Instructional Strategies Part of Chapter 3 Number Theory and Fractions (3.1-3.3)

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.

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. 4 2  Continue until only prime numbers remain. 2 2  Write prime factorization in exponential form. 56 = 23•7

Let’s 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

Let’s Use the Ladder for LCM and GCD with 3 or more numbers  WRITE the two numbers on one line. 4 6 2 12 x  DRAW THE L SHAPE 3 2 3 6  DIVIDE out common prime numbers (at least 2 must be in common) x 2 2 1 2 *Numbers that can not be divided out, CIRCLE and bring STRAIGHT down 1 1 1  LCM makes an L: LCM = 2  3  2  1  1  1 = 12 *If a number is circled, cross out the divisor that corresponds, and do not use it to find the GCD. GCF* is down the left side: GCF = 2

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