# All Lessons

### Use the Relationship Between Multiplication & Division

4.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.

4.NBT.64.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-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.

This number sense lesson focuses on using the relationship between multiplication and division to check answers. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students identify the operation needed to check the answer. Then, they set up the multiplication or division problem and identify the numbers used to create the problem. Then, students check the answer by solving the problem. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Use Addition 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).

1.NBT.41.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

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.

### 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.

### Use Multiplication Strategies

(E) Represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

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

3.4.G(G) Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

4.4.D(D) Use strategies and algorithms, including the standard algorithm, to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

(Y2) Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)

ACMNA075(Y4) Recall multiplication facts up to 10 × 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)

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

3.NBT.33.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 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.

### 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 × 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 ÷ 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 ÷ 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 × 5 = 40, one knows 40 ÷ 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.

### Add Fractions with Like Denominators

This number and operations -- fractions lesson teaches students how to add fractions with like denominators. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will add fractions with like denominators. This lesson includes a variety of real-world examples. This lesson also covers reducing fractions.

### Subtract Fractions with Like Denominators

This number and operations -- fractions lesson teaches students how to subtract fractions with like denominators. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will subtract fractions with like denominators. This lesson includes a variety of real-world examples. This lesson also covers reducing fractions.

### Add Mixed Numbers With Like Denominators

This Common Core number and operations -- fractions lesson focuses on adding mixed numbers with like denominators. The lesson includes research-based strategies and strategic questions that prepare students for Common Core assessments. In this lesson, students will read the problem aloud, identify the whole numbers and fractions, and write them as an addition problem. Then, they will combine the sum of both problems to determine the answer. Finally, they will reduce the fraction or regroup, if needed. In addition to the lesson, there are four pages of Independent Practice with questions modeled after the Common Core assessment items.

### Use Pictures to Add Fractions

This number sense lesson focuses on using pictures to add fractions. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students represent the sum of the fractions by shading the number of equal parts. Then, they add fractions by using the pictures (keeping the common denominator and finding the numerator by adding the number of equal parts). In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Use Pictures to Subtract Fractions

This number sense lesson focuses on using pictures to subtract fractions. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students represent the difference of the fractions by shading the number of equal parts. Then, they subtract fractions by using the pictures (keeping the common denominator and finding the numerator by subtracting the number of equal parts). In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Add Fractions With a Common Denominator

4.NF.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.3.D4.NF.3.D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

This number sense lesson focuses on adding fractions with a common denominator. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students read the problem and make sure both fractions have a common denominator. Then, they find the sum of the fractions by keeping the denominator the same, adding the numerators, and then representing the sum by shading in the figure. Then, they determine if the sum can be shown by an equivalent fraction using lower numbers, and shading in the figure. Finally, students read the addition problem with the sum. In addition to the lesson, there are eight pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Subtract Fractions with a Common Denominator

4.NF.3.A Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.3.D4.NF.3.D Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

This number sense lesson focuses on subtracting fractions with a common denominator. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students read the problem and make sure both fractions have a common denominator. Then, they find the difference of the fractions by keeping the denominator the same, subtracting the numerators, and then representing the difference by shading in the figure. Then, they determine if the difference can be shown by an equivalent fraction using lower numbers, and shading in the figure. Finally, students read the subtraction problem with the difference. In addition to the lesson, there are eight pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Write Decimal Numbers as Fractions (Tenths & Hundredths)

This number sense lesson focuses on writing decimal numbers as fractions. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students identify the digit in the lowest place value and read the decimal number aloud. Then, they write the decimal number as a fraction and interpret the decimal number and the fraction. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Identify Mixed Numbers on a Number Line

This number sense lesson focuses on identifying mixed numbers on a number line. The lesson includes research-based strategies and questions that help prepare students for assessments. In this lesson, students identify the mixed numbers on the number line and determine which two whole numbers the mixed number is between on the number line, and identify the fraction of the mixed number between the two whole numbers. Finally, students interpret their results. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.

### Generate Equivalent Fractions

This number and operations--fractions lesson teaches students how to generate equivalent fractions. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will create equivalent fractions. This lesson focuses on changing a fraction to another. Students are provided a variety of strategies and support to visualize the equivalence. Real-world examples are also provided.

### Fraction Word Problems: Multiplication

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

### Fraction Word Problems: Addition and Subtraction

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

### Add Fractions with Denominators 10 & 100

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.* For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

### Perimeter & Area Formulas

This measurement and data lesson requires students to solve problems by applying the area and perimeter formulas for rectangles. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students are taught the formulas for area and perimeter and then are given word problems and diagrams and asked to find the perimeter and/or area. Students are also required to read a word problem and determine whether they need to solve for area or perimeter based on the given information.

### Find the Perimeter of a Rectangle

This measurement and geometry lesson focuses on finding the perimeter of a rectangle. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem to find the rectangle's length and width. Then, they substitute the rectangle's length and width into the perimeter formula and compute the perimeter. Finally, they label the answer with the correct unit of measurement. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.