Gr+6-7+Math

Participants: Mel F., Karen G. Carole H.

Subject: Mathematics Topic: Surface Area (adapted from Cathy Fosnot) Grade: 6 and 7

Type of Critical Thinking Challenge: Design to specs (Students design a product that meets a given set of criteria/ conditions)

Critical Challenge (Question or Task): What is the most effective way to package 24 truffles in a rectangular box?

Context: Every one is buying chocolates this time of year. You are going to be part of a company that needs to show a chocolate maker the most cost effective way to design a box for 24 chocolates. The chocolates are cubes that are 1cm² by 1cm² by 1cm². Your group initially needs to design a variety of different possible boxes. Then select your best box design and make a proposal to the president of the company explaining how you and your group have arrived at the most effective way to package 24 truffles in rectangular boxes. The cost of the material to make the boxes is $0.05 per cm².

Evidence of Learning: ➢students will be able calculate and apply their knowledge of surface area to find a wide variety of boxes that would fit 24 chocolates ➢students will be able to calculate the cost of the different boxes using the surface area and rate ➢students will be able to organize and explain their solutions and identify the most cost effective box

Key Learning:

Students will apply their knowledge of surface area in a real life context using rates (price per cm²).

Big Ideas (Big Ideas from Doctor Small) Length and Area (Pg. 136) ➢The length of an object is a one- dimensional attribute, i.e. the number of linear units along a line or curve on the object. Length can be the measurement of a single measure of the object of a combined linear measure, like perimeter.

➢The area of an object is a two-dimensional attribute, i.e., the number of square units it takes to cover a shape on a surface of an object. Area can be a single measure of a 2-D shape of an object of combined measure of a 3-D shape, like surface area.

Proportional Thinking: Rate, Ratio and Percent (Pg. 74)

➢Ratios, rates, and percents, just like fractions and decimals, are comparison of quantities. (a rate compares quantities with different units, for example, distance to time, or price per number of items)

Overall Expectations Evaluated || Measurement -estimate, measure, and record quantities, using the metric measurement system -determine the relationships among units and measurable attributes, including the area of a parallelogram, the area of a triangle and the volume of a triangular prism

Numeration -demonstrate an understanding of relationships involving percent, ratio, and unit rate || Specific Expectations Addressed || Measurement -determine through investigation using a variety of tools and strategies, the surface area of rectangular and triangular prisms -solve problems involving the estimation and calculation of the surface area and volume of triangular and rectangular prisms

Numeration -represent relationships using unit rates ||

Requisite Tools: Background Knowledge || * how to calculate the area of a rectangle || Criteria for Judgement || * most cost effective (least price) || Critical Thinking Vocabulary ||  * criteria ( ability to find the most effective cost and their ability to clearly communicate their findings using appropriate
 * design a net of a rectangle prism
 * how the dimensions of a rectangular prism relate to volume and surface area
 * how to calculate surface area of a rectangular prism
 * the definition of "cost effective"
 * how to calculate cost per cm² (rate)
 * precision (calculate the surface area and cost based on the rate of $0.05 per cm²)
 * effective communication (identifies and defends their most cost effective package for 24 chocolates)

vocabulary and conventions) || Thinking Strategies ||  * isometric drawings (instead of having to draw nets)  || Habits of Mind  ||  * consultative (students work in small groups to confer with others about ideas)  ||
 * judgement (students have to decide which design is the most cost effective)
 * evaluating (students have to decide and explain their choice)
 * chart to organize solutions
 * critically minded (students will continually evaluate their work when necessary)
 * attentive to detail (is able to communicate written and oral presentation with details)
 * persistence (persists through the challenge)

Please note: Students will work in small groups of 2 to 3 students, all of their work is done on chart paper so that their work is large enough to be visible to the class when presenting.


 * Overall Expectations Evaluated || __ Measurement __

-estimate, measure, and record quantities, using the metric measurement system -determine the relationships among units and measurable attributes, including the area of a parallelogram, the area of a triangle and the volume of a triangular prism

__ Numeration __

-demonstrate an understanding of relationships involving percent, ratio, and unit rate ||