## In mathematics Students Should be able to...

STANDARDS FOR MATHEMATICAL PRACTICE

1. Make sense of problems and persevere in solving them. Students make sense of real-world fraction and decimal problem situations by representing the context in tactile and/or virtual manipulatives, visual, or algebraic models.

2. Reason abstractly and quantitatively. Students will apply the constructs of multiplication, division, addition, and subtraction of rational numbers to solve application problems.

3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding the portion of a whole as represented in the context of real-world situations. Students explain why they do not always get a smaller number when dividing with fractions and decimals. Students have to reason the steps in modeling division of fractions.

4. Model with mathematics. Students will model real-world situations to show division of fractions. Students use number lines and tape diagrams to find least common multiple and greatest common factor.

5. Use appropriate tools strategically. Students will use visual or concrete tools for division of fractions with understanding.

6. Attend to precision. Students attend to the language of problems to determine appropriate representations and operations for solving real-world problems. In addition, students attend to the precision of correct decimal placement used in real-world problems.

7. Look for and make use of structure. Students examine the relationship of rational numbers (positive decimal and fraction numbers) to the number line and the place value structure as related to multi-digit operations. They also use their knowledge of problem solving structures to make sense of word problems.

8. Look for and express regularity in repeated reasoning. Students demonstrate repeated reasoning when dividing fractions by fractions and connect the inverse relationship to multiplication. Students also use repeated reasoning when solving real-world problems using rational numbers.

1. Make sense of problems and persevere in solving them. Students make sense of real-world fraction and decimal problem situations by representing the context in tactile and/or virtual manipulatives, visual, or algebraic models.

2. Reason abstractly and quantitatively. Students will apply the constructs of multiplication, division, addition, and subtraction of rational numbers to solve application problems.

3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding the portion of a whole as represented in the context of real-world situations. Students explain why they do not always get a smaller number when dividing with fractions and decimals. Students have to reason the steps in modeling division of fractions.

4. Model with mathematics. Students will model real-world situations to show division of fractions. Students use number lines and tape diagrams to find least common multiple and greatest common factor.

5. Use appropriate tools strategically. Students will use visual or concrete tools for division of fractions with understanding.

6. Attend to precision. Students attend to the language of problems to determine appropriate representations and operations for solving real-world problems. In addition, students attend to the precision of correct decimal placement used in real-world problems.

7. Look for and make use of structure. Students examine the relationship of rational numbers (positive decimal and fraction numbers) to the number line and the place value structure as related to multi-digit operations. They also use their knowledge of problem solving structures to make sense of word problems.

8. Look for and express regularity in repeated reasoning. Students demonstrate repeated reasoning when dividing fractions by fractions and connect the inverse relationship to multiplication. Students also use repeated reasoning when solving real-world problems using rational numbers.

## __PARENTS LOOK HER__E! UNIT 1 is 9 to 10 weeks (AUG 10 - October 16th)

TOPIC: NuMBER FLUENCY & INTRO TO RATIOS

**In this unit students will:**

• Find the greatest common factor of two whole numbers less than or equal to 100.

• Find the least common multiple of two whole numbers less than or equal to 12.

• Find the prime factorization of whole numbers.

• Introduction to understanding ratios

• Find the greatest common factor of two whole numbers less than or equal to 100.

• Find the least common multiple of two whole numbers less than or equal to 12.

• Find the prime factorization of whole numbers.

• Introduction to understanding ratios

**• Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.**

• Interpret and compute quotients of fractions.

• Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem.

• Fluently divide multi-digit numbers using the standard algorithm.

• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

• Interpret and compute quotients of fractions.

• Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem.

• Fluently divide multi-digit numbers using the standard algorithm.

• Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

## UNIT 1 RESOURCES

## PARENTS LOOK HERE! UNIT 2 IS 9 to 10 weeks (OCT. 19th - Dec. 18th)

TOPIC: Rate, RATIO and PROPORTIONAL REASOning

**In this unit students will:**

**Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.****Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.****Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.****Make tables of equivalent ratios relating quantities with whole-number measurements, ﬁnd missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.****Solve unit rate problems including those involving unit pricing and constant speed.****Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.****Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.**

## UNIT 2 RESOURCES

## Parents Look Here! UNIT 3 is 4 to 5 weeks (JAN 6th - FEB 12th)

TOPIC: AREA AND VOLUME

In this unit students will:

- Find area of right triangles, other triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
- Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths (1/2 u), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = (length) x (width) x (height) and V= (area of base) x (height) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
- Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.