## Summary

Students will solve story problems that involve addition, subtraction,multiplication, and division with decimals. Students will representparts of a dollar as a fraction, a decimal, and a percentage.

## Objectives

- Students will solve story problems that involve addition, subtraction, multiplication, and division with decimals.
- Students will represent parts of a dollar as a fraction, a decimal, and a percentage.

## Subject Area

- Math

## Grades

- 4th
- 5th
- 6th

## Class Time

- Total Time: 91-120 minutes

## Materials

- Copies of the "How Much?" worksheets
- Problem(s) to be solved as a group, projected or on handouts
- Paper and pencil
- Math manipulatives, such as pattern blocks or fraction bars (optional)

## Lesson Steps

- Begin with a quick review of decimals, fractions, and percentages.
- Hand out the "How Much?" worksheet. Display or hand out problem(s) to be solved as a whole group. Read the first problem together. Discuss some different strategies one might use to solve the problem. (Allowing students to think about their own strategies for solving the problems will encourage them to think independently and critically about numbers and will serve to improve their understanding of operations and number sense.)
- Use one of the suggested strategies for the first problem and work it through on the overhead so that all students can see your work. Discuss whether the answer is correct and how the strategy worked.
- Ask students to work through the other three story problems on their own or in small groups. Once students have finished the problems, reconvene and go over the strategies used and the solutions. Depending on the skill level of the students, the teacher may wish to work all problems as a group. Discuss how many different strategies for solving problems can produce accurate answers. Ask students to think about which of the strategies they saw were the most efficient and effective in getting the correct answers.
- Demonstrate how to convert amounts into fractions, percentages, and decimals. For practice, ask students to complete question 5 on the "How Much?" work page on their own or in small groups.

## Assess

Use the worksheets and class participation to assess whether the students have met the lesson objectives.

## Common Core Standards

**Discipline**: Math

**Domain**: 4.MD Measurement and Data

**Grade(s)**: Grade 4

**Cluster**: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit

**Standards**:

**4.MD.1.**Know relative sizes of measurement units within one system of units including km, m, cm, kg, g, lb, oz, l, ml, hr, min and sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table.- For example, know that 1ft is 12 times as long as 1in. Express the length of a 4ft snake as 48in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

**4.MD.2.**Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.**4.MD.3.**Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

**Discipline**: Math

**Domain**: 5.MD Measurement and Data

**Grade(s)**: Grade 4

**Cluster**: Represent and interpret data

**Standards**:

**5.MD.2.**Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

## National Standards

**Discipline**: Mathematics

**Domain**: All Problem Solving

**Cluster**: Instructional programs from kindergarten through grade 12 should enable all students to

**Grade(s)**: Grades K–12

**Standards**:

- Build new mathematical knowledge through problem solving
- Solve problems that arise in mathematics and in other contexts
- Apply and adapt a variety of appropriate strategies to solve problems
- Monitor and reflect on the process of mathematical problem solving

**Discipline**: Mathematics

**Domain**: 3-5 Number and Operations

**Cluster**: Compute fluently and make reasonable estimates.

**Grade(s)**: Grades K–12

**Standards**: In grades 3–5 all students should

- develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50;
- develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
- develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
- develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
- use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; and
- select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

**Discipline**: Mathematics

**Domain**: 3-5 Number and Operations

**Cluster**: Understand meanings of operations and how they relate to one another.

**Grade(s)**: Grades K–12

**Standards**: In grades 3–5 all students should

- understand various meanings of multiplication and division;
- understand the effects of multiplying and dividing whole numbers;
- identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; and
- understand and use properties of operations, such as the distributivity of multiplication over addition.

**Discipline**: Mathematics

**Domain**: 3-5 Number and Operations

**Cluster**: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

**Grade(s)**: Grades K–12

**Standards**: In grades 3–5 all students should

- understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
- recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
- develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
- use models, benchmarks, and equivalent forms to judge the size of fractions;
- recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
- explore numbers less than 0 by extending the number line and through familiar applications; and
- describe classes of numbers according to characteristics such as the nature of their factors.

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