# All Lessons

## Fluently Add and Subtract

(G) Apply properties of operations to add and subtract two or three numbers.

2.4.A(A) Recall basic facts to add and subtract within 20 with automaticity

(Y2) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

ACMNA055(Y3) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

Algebra Textbook Chapter 1

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## Fluently Multiply

(F) Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

4.4.B(B) Determine products of a number and 10 or 100 using properties of operations and place value understandings

(Y3) Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

ACMNA075(Y4) Recall multiplication facts up to 10 Ã— 10 and related division facts (ACMNA075)

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 Ã— 80, 5 Ã— 60) using strategies based on place value and properties of operations.

4.NBT.54.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Algebra Textbook Chapter 1

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## Use Subtraction Strategies

(Y2) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

ACMNA055(Y3) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.61.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

2.OA.22.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

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## Use Division Strategies

(F) Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

3.4.J(J) Determine a quotient using the relationship between multiplication and division

3.5.B(B) Represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

5.3.C(C) Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm

(Y2) Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)

ACMNA075(Y4) Recall multiplication facts up to 10 Ã— 10 and related division facts (ACMNA075)

ACMNA076(Y4) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

ACMNA101(Y5) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 Ã· 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 Ã· 8.

3.OA.73.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 Ã— 5 = 40, one knows 40 Ã· 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

5.NBT.65.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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## Use Exponent Rules to Multiply

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 Ã— 3-5 = 3-3 = 1/33 = 1/27.

HSA.APR.1HSA.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Lesson 9.2

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## Cross Multiplication

7.RP.2 Recognize and represent proportional relationships between quantities.

7.RP.2.C7.RP.2.C Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

HSA.REI.2HSA.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.