- Students will determine the information they need to solve a problem.
- Students will use the guess and check method to solve their problem.
- Students will test their answer using this method with real coins.
- Total Time: 0-45 Minutes minutes
- Web sites with math problem-solving strategies such as https://mylearningspringboard.com/problem-solving-strategies/
- Math journals
- Circulating coins
- Explain to the students that there are many different strategies for solving math problems. It is important to know the strategies, and also to know when to use which strategy. Tell them that they will be using the Guess, Check and Revise method.
- As a class, discuss how many different combinations of circulating coins (nickels, dimes and quarters) can be used to add up to 50 cents. You must use at least one of each coin. Have the students make a guess and write several guesses on the board.
- Write out the specifics of the problem: To make 50 cents using only nickels, dimes and quarters, at least one of each coin.
- Work with your students to develop a chart with the possible solutions. There will only be two solutions for this problem (1 quarter 2 dimes and a nickel; 1 quarter, 1 dime and 3 nickels). Students can then revise their answer based on the chart.
- Now give the students a problem to solve on their own using the same method you did as a class. Have them record the steps in their math journal. For example: How many different combinations of nickels, dimes and quarters can make $2.25 when you must use 17 coins.
Common Core 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.
- 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 3–5 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 3–5 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.
Discipline: Mathematics Domain: All Problem Solving Cluster: Instructional programs from kindergarten through grade 12 should enable all students to Grade(s): Grades 3–5 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