NCDPI AIG Instructional Resource: Background Information s11

NCDPI – AIG Instructional Resource: Background Information

Resource Title: Puzzle Building

Subject Area/Grade Level (s): Math/5 Time Frame: 1 class period

Common Core/Essential Standard Addressed: Number and Operations-Fractions Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. b. Interpret division of a whole number by a unit fraction, and compute such quotients. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 6. Attend to precision.

Additional Standards Addressed: NA

Brief Description of Lesson/Task/Activity: Students will determine which distributor (of a small company that produces wooden children’s puzzles) they should purchase their materials from. Students will use their understanding of fractions in order to determine the number of given lengths of wood that can be extracted from the sizes of dowel rods and boards that the distributors offer.

Type of Differentiation for AIGs (include all that apply): Enrichment x Extension x Acceleration

Adaptations for AIGs: x Content Process x Product

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project Explanation of How Resource is Appropriate for AIGs: This resource is appropriate for gifted students as it provides a real world context for dividing fractions and requires that they extend their understanding of dividing whole numbers by fractions and apply that knowledge to dividing whole numbers by mixed numbers. Students are also required to compare the prices of two different distributors in order to determine which distributor the puzzle company should do business with. This task is accessible for students who are not fluent with the standard algorithm for dividing fractions as well as those who are.

Needed Resources/Materials:  Pictures of wooden children’s puzzles, dowel rods, and various pieces of wood for purchase  Real wooden puzzle (optional)

Sources: NA

TEACHER NOTES: NA

NCDPI AIG Curriculum Resource Outline

STAGE ONE: ENGAGE

Have students read the scenario… The Purple Puzzle, a small company that builds and sells wooden children’s puzzles, has a dilemma. There are two local distributors who sell the materials they need to build their puzzles. The materials come in different sizes and have different prices from the two distributors. The owners of the Purple Puzzle need your help in determining which distributor they should buy their materials from. Have students read the scenario independently before asking these questions… 1. What do you know from the information provided? 2. What terms/vocabulary/words need clarification? 3. What factors should be considered when deciding which company to purchase materials from? 4. Are there other factors we need to keep in mind?

STAGE TWO: ELABORATE

Once students have had time to discuss the scenario and any terms or ideas that may be unfamiliar, present the list of materials needed and each distributing company’s prices.

The Purple Puzzle builds each puzzle from the same materials. Each puzzle requires nine dowel rods, ¾ inch in length, to make the handles of each puzzle piece. Each of the nine puzzle pieces is created from wood, ½ in. thick, 3 ½ in. wide, and 3 ½ in. long. The puzzle pieces fit into a border made from wood that is 1 in. thick, 1 ½ ft. wide, and 1 ft. long.

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project Dazzling Distributors sells 5 ft. dowel rods for $2.25 each. They sell ½ in. by 3 ½ in. boards that are 8 ft. long for $9.45. Boards that are 1 in. thick and 1 ½ ft. wide come in lengths of 8 ft. and are priced at $12.75 each. A standard delivery fee of $150 is applied to all orders.

Wood Wonders sells 6 ft. dowel rods for $2.95 each and ½ in. by 3 ½ in. boards that are 6 ft. long for $8.30. Boards that are 1 in. thick and 1 ½ ft. wide come in lengths of 10 ft. and are priced at $15.75 each. A delivery fee of $15 per mile (one way) is applied to all orders. The Purple Puzzle is 9 miles from Wood Wonders.

Pose the following questions (as needed)…  How could you organize the information in order to make your calculations easy to analyze?  On what will you base your choice of distributor to purchase materials from?  Should everyone have the same answer? Explain your thinking.  If a non-whole number of pieces can be made from the lengths in which the materials are sold, what should you do?

STAGE THREE: EVALUATE

Have students determine the answers to the following questions based on the information given about the 2 companies. Student work should be evaluated based on accuracy of calculations, their ability to estimate when necessary, their understanding of operating on fractions, whole numbers, and mixed numbers, use of mathematical vocabulary, and articulation of their choice of company as evidenced in their work. Students may respond to the task in their math notebooks, or the teacher may choose to have students compose a letter to the Purple Puzzle advising the owners of the distributing company they feel is most appropriate based on mathematical findings.

Students should address the following questions and provide evidence for each response. 1. The Purple Puzzle just received an order for 400 puzzles! How much of each building material (dowel rod, ½ in. by 3 ½ in. board, and 1 in. thick and 1 ½ ft. wide board) will they need? 2. Determine the total cost (including the delivery fee) of the materials needed to build 400 puzzles from each distributing company. 3. Based on your calculations, should the Purple Puzzle order their supplies from Dazzling Distributors or Wood Wonders? Support your answer using clear mathematical reasoning and precise vocabulary. 4. Determine the cost of making 1 puzzle with materials from each of the distributing companies. 5. How do your findings in problem 4 support or negate your choice of company from problem 3?

TEACHER NOTES: NA

PUBLIC SCHOOLS OF NORTH CAROLINA State Board of Education | Department of Public Instruction AIG ~ IRP Academically and/or Intellectually Gifted Instructional Resources Project