Math at Work 11 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Math at Work 10 - 12 and related Math 7 - 9 Outcomes *Updated May 2024*
A01 - This is not an outcome that can be taught in isolation but must be integrated as a foundational concept within each of the units in the course.
M01 Students will be expected to solve problems that involve SI and imperial units in surface area measurements and verify the solutions. [C, CN, ME, PS, V]
M01.01 Explain, using examples, the difference between volume and surface area.
M01.02 Explain, using examples, including nets, the relationship between area and surface area.
M01.03 Explain how a referent can be used to estimate surface area.
M01.04 Estimate the surface area of a 3-D object.
M01.05 Illustrate, using examples, the effect of dimensional changes on surface area.
M01.06 Solve a contextual problem that involves the surface area of 3-D objects, including spheres, and that requires the manipulation of formulas.
M02 Students will be expected to solve problems that involve SI and imperial units in volume and capacity measurements. [C, CN, ME, PS, V]
M02.01 Explain, using examples, the difference between volume and capacity.
M02.02 Identify and compare referents for volume and capacity measurements in SI and imperial units.
M02.03 Estimate the volume or capacity of a 3-D object or container, using a referent.
M02.04 Identify a situation where a given SI or imperial volume unit would be used.
M02.05 Solve problems that involve the volume of 3-D objects and composite 3-D objects in a variety of contexts.
M02.06 Solve a problem that involves the capacity of containers.
M02.07 Write a given volume expressed as another unit in the same measurement system.
M02.08 Write a given capacity expressed as another unit in the same measurement system.
M02.09 Determine the volume of prisms, cones, cylinders, pyramids, spheres, and composite 3-D objects using a variety of measuring tools such as rulers, tape measures, calipers, and micrometers.
M02.10 Determine the capacity of prisms, cones, pyramids, spheres, and cylinders, using a variety of measuring tools and methods, such as graduated cylinders, measuring cups, measuring spoons, and displacement.
M02.11 Describe the relationship between the volumes of cones and cylinders with the same base and height pyramids and prisms with the same base and height
M02.12 Illustrate, using examples, the effect of dimensional changes on volume.
M02.13 Solve a contextual problem that involves the volume of a 3-D object, including composite 3-D objects, or the capacity of a container.
M02.14 Solve a contextual problem that involves the volume of a 3-D object and requires the manipulation of formulas.
A01 Students will be expected to solve problems that require the manipulation and application of formulas related to
volume and capacity
surface area
slope and rate of change
simple interest
finance charges
[C, CN, PS, V]
A01.01 Solve a contextual problem involving the application of a formula that does not require manipulation.
A01.02 Solve a contextual problem involving the application of a formula that requires manipulation.
A01.03 Explain and verify why different forms of the same formula are equivalent.
A01.04 Describe, using examples, how a given formula is used in a trade or an occupation.
A01.05 Create and solve a contextual problem that involves a formula.
A01.06 Identify and correct errors in a solution to a problem that involves a formula.
Additional Resources and Activities for M01 and A01 (surface area):
3 Acts - Pop Box Design and Introducing Surface Area with Pop Box Design - Pop boxes come in various dimensions. Which one is the most efficient? Why would a company not select the most efficient design?
Designing Candy Cartons from Mathematics Assessment Project (MAP) - Students design and create a carton to package 18 cylindrical candies. Students then share why they designed their package a specific way and how they made sure that all 18 candies would fit.
Additional Resources and Activities for M02 and A01 (volume and capacity):
Smarties Part 1 and Smarties Part 2 - How many Smarties would you expect in a 45g box? What is the cost per gram or cost per Smartie? Why is there so much empty space in a Smarties box? Can you create a more efficient package with less empty space? The activities contain the unit price outcome from Math at Work 10 as well as work with interpolating and Extrapolating Values from MTW11 Stats and Nets and Surface Area of 3-D Objects from the MTW11 Measurement unit.
Largest Box Problem - Make the largest (volume) single open box using the grid sheet (20 cm by 16 cm). You may cut and paste the sheet to get your perfect box but the sides of each box should be made from a single sheet of paper. Plan before you cut.
Cylinders Open Middle Problem - Find 3 different cylinders that hold between 110 and 115 cu. ft. of water.
Expanding Cylinders - To increase the volume of a cylinder, is it better to increase the radius or the height? Great conversation starter.
Volume of a Pyramid - Develop the formula for the volume of a pyramid via an investigation using templates to cut out shapes that decompose from a prism into 3 pyramids. A cube in three parts and a rectangular prism in six parts.
Desmos Activity: Volume comparisons with prisms and pyramids, cones and cylinders - Based on Prisms and Pyramids - A 3-Act math task to find out how many pyramids it takes to fill a prism with the same height.