# Simple Strategies

### Summary

Students will be able to make a diagram, identify a pattern, and work backwards to solve mathematical word problems. They will also explore money concepts such as budgeting and spending.

### Coin Type(s)

- Quarter

### Coin Program(s)

- 50 State Quarters

### Objectives

- Students will be able to make a diagram, identify a pattern, and work backwards to solve mathematical word problems.
- They will also explore money concepts such as budgeting and spending.

### Major Subject Area Connections

- Language Arts
- Math

### Grades

- Second grade
- Third grade

### Class Time

**Sessions**: Three

**Session Length**:
30-45 minutes

**Total Length**:
91-120 minutes

### Groupings

- Whole group
- Pairs
- Individual work

### Background Knowledge

Students should have a basic knowledge of:

- Addition
- Subtraction
- Patterns
- Coins
- Coin values

### Terms and Concepts

- Quarter
- Reverse (back)
- Problem Solving
- Make a Diagram
- Identify Patterns
- Work Backwards

### Materials

- 1 copy of an age-appropriate text relating to problem solving, such as:
*Penny Pot*by Stuart J. Murphy*Chair For My Mother*by Vera B. Williams*The Best Vacation Ever*by Stuart J. Murphy*Upside-Downside, Downside-Upside*by Pat Canady*I Want It*by Elizabeth Crary, Marina Megale*What Do You Think? The Book of Problem Solving*by Jack Wasserman, Selma Wasserman, Dennis Smith

- Chalkboard/chalk
- Chart paper/markers
- 1 overhead transparency of the Problem Solving Strategies page
- 1 overhead projector
- Practice Problem Solving pages
- Strategize! page
- Strategize! Key page

### Preparations

- Make copies of the following:
- Practice Problem Solving packets (1 per student)
- Strategize! page (1 per student)
- Strategize! Key page (1 copy)
- Make an overhead transparency of the Problem Solving Strategies page.

- Locate an age-appropriate text relating to problem solving (see examples under "Materials").

### Worksheets and Files

Lesson plan, worksheet(s), and rubric (if any) at www.usmint.gov/kids/teachers/lessonPlans/pdf/275.pdf.

**Session 1 **

- Discuss problem solving with students. Give a personal account of a time that you have solved a problem in your life. Then, have students share similar stories.
- Introduce the selected text. Ask the students to generate predictions about what is occurring during different parts of the story.
- Read the text aloud to the group. During the reading, attend to any unfamiliar vocabulary.
- Have the students identify different strategies the characters used in trying to solve their problems.
- Write the following word problem on the board: "Frank and Maureen went to the grocery store. Frank bought four apples. Maureen bought two apples. How many apples did they buy in all?"
- Ask the students to identify the very first thing they need to do in order to solve this problem. Guide the students to respond that they need to read the problem first.
- Label a piece of chart paper "Steps of Problem Solving." Underneath the title, write "Step 1: READ the problem."
- Read the problem aloud to the class.
- Explain to the students that the next thing to do in order to solve this problem is to identify the important information that’s been given.
- On the piece of chart paper, write "Step 2: Underline GIVEN information."
- Reread the problem aloud and have the students identify important words or phrases. Student responses should include that Frank has four apples and Maureen has two. Underline the sentences "Frank bought four apples" and "Maureen bought two apples" on the board.
- Explain to the students that the next thing to do in order to solve this problem is to identify what the problem is asking them to do.
- On the piece of chart paper, write "Step 3: Circle the QUESTION."
- Reread the problem aloud and have the students identify what the problem is asking them to do. The students should respond that the problem is asking them to figure out how many apples Maureen and Frank bought altogether. Circle the question on the board.
- Explain to the students that the next thing to do in order to solve the problem is to answer the question that the problem is asking.
- On the piece of chart paper, write "Step 4: Choose a STRATEGY to solve the problem."
- Discuss with the students how to solve the problem. Have the students consider whether they need to add or subtract numbers. Guide the students to respond that the words "in all" are a hint that addition is involved. Then, have the students consider what numbers should be added together. Guide the students to respond that Frank’s apples plus Maureen’s apples will give them the total number of apples.
- Explain to the students that the last thing to do is to solve the problem. On the piece of chart paper, write "Step 5: SOLVE the problem."
- Direct the students to find the answer to the question with a partner. Have the students pay close attention to how they solve the problem.
- Have the students share their answers with the class. Explain, if necessary, that the correct answer is that Maureen and Frank bought six apples in all.
- Lead a class discussion on the process that the students followed to find their answers. Record the student responses on the board.
- Explain to the students that there are a lot of different ways to solve any problem. Explain that, in the coming days, the students will experiment with different ways to solve problems.

**Session 2 **

- Review the "Steps of Problem Solving" chart paper from the previous session. Ask the students to recall and discuss what each step means.
- Remind the students of the problem from the previous session. Explain to the students that, in this session, they will be exploring different ways to solve problems.
- Display an overhead transparency of the "Problem Solving Steps" page. Explain that these are just some of the problem solving strategies that students can use.
- Read each strategy aloud and have the students predict what each one means.
- Distribute one "Practice Problem Solving" packet to each student.
- Read the first strategy aloud. Then, have a student read the word problem aloud. Direct the students to underline the important information and circle the question. Then, explain how to execute this problem solving strategy. Write and draw on the board as necessary as students follow along. Have the students solve the problem and share their answers. Answer student questions.
- Direct the students to complete the two practice examples for this problem solving strategy individually or with a partner. Review each example as a class.
- Repeat steps 6 and 7 for each of the problem solving strategies.
- Explain to the students that, in the following session, they will work together in groups to solve problems by selecting the appropriate problem solving strategy.

**Session 3 **

- Have the students recall the three problem solving strategies they learned in the previous session. Write each strategy on the board. Have the students discuss all the strategies and how they work.
- Review the problem solving steps with the students. Keep the chart paper that the steps are listed on visible for the rest of the session.
- Write the following problem on the board: "There are three coins on a desk. Two are nickels. The total value of the coins is 20 cents. What is the other coin?"
- Have the class read the problem aloud, underline the important information, and circle the question.
- Direct the students to select a strategy and solve the problem.
- Have the students share which strategy they used to solve the problem. Point out that both the "making a diagram" and "working backwards" strategies are effective in solving this problem.
- Have a student show on the board how each of the strategies could solve the problem.
- Explain to the students that they will be working in groups to solve word problems using the strategy that makes the most sense to them.

### Differentiated Learning Options

- Students needing extra support with problem solving can practice by visiting one of the following websites: – www.abcteach.com/Reading/suess/math1.htm
- Create a study guide for students, outlining each of the problem solving strategies.

### Enrichments/Extensions

- Direct students to create their own word problems. On a separate piece of paper, stu-dents can show which strategy would work for this problem and include the correct answer. Students can then swap problems and challenge each other.
- Groups that finish the "Strategize!" activity early can go back and try to solve the same problems using different strategies.

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

**Discipline**: Math

**Domain**: 2.OA Operations and Algebraic Thinking

**Grade(s)**:
Grade 2

**Cluster**: Add and subtract within 20

**Standards**:

- 2.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, eg, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

**Discipline**: Math

**Domain**: 2.OA Operations and Algebraic Thinking

**Grade(s)**:
Grade 2

**Cluster**: Represent and solve problems involving addition and subtraction.

**Standards**:

**2.OA.1.**Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, eg, by using drawings and equations with a symbol for the unknown number to represent the problem.

**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**: K-2 Number and Operations

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

**Grade(s)**:
Grades K–12

**Standards**:

In K through grade 2 all students should

- develop and use strategies for whole-number computations, with a focus on addition and subtraction;
- develop fluency with basic number combinations for addition and subtraction; and
- use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

**Discipline**: Mathematics

**Domain**: K-2 Number and Operations

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

**Grade(s)**:
Grades K–12

**Standards**:

In K through grade 2 all students should

- understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;
- understand the effects of adding and subtracting whole numbers; and
- understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.