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- Mathematics: 10th Grade
Ontario - Mathematics: 10th Grade
ON--Locally Developed Compulsory Credit Courses | Adopted: 2005
EMSV: : Extending Money Sense
EMSV.01: : solve problems drawn from everyday situations involving money, demonstrating skill, and understanding in the use of decimal numbers;
1.1.1: : Understanding and Using Decimal Numbers in Solving Problems
EMS1.06: : solve problems involving sales tax, discounts, restaurant tips, and commission earnings (e.g., A skateboard costs $49.99 before taxes. You have $60.00. Do you have enough to buy the skateboard? Justify your answer.);
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
EMS1.08: : solve problems involving the accomplishment of a particular goal, including investigating, planning, gathering, and organizing data, and making relevant calculations (e.g., plan a special event within a given budget).
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
EUMV: : Extending Understanding of Measurement
EUMV.01: : make estimates and measurements to extend understanding of the metric system;
2.1.1: : Estimating and Measuring Using the Metric System
EUM1.03: : estimate, using standard units, measurements of length, capacity, and mass that arise from their everyday experience (e.g., the distance from school to the motor vehicle office is about 15 km; the mass of the refrigerator is about 75 kg; the capacity of a gasoline tank is about 60 L);
Beam to Moon (Ratios and Proportions) - Metric
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
EUM1.08: : describe applications from everyday life and the workplace that involve a combination of perimeter, area, volume, mass, capacity, time, and/ or money (e.g., a landscaping project may require the use of perimeter for purchasing fencing, area for purchasing sod, volume for purchasing soil, and require the job to be completed within a specified time).
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Beam to Moon (Ratios and Proportions) - Metric
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
EUMV.03: : solve problems involving measurements of circles, rectangles, cylinders, and rectangular prisms, using metric units in applications drawn from everyday life and the workplace;
2.3.1: : Solving Problems Involving Circumference, Perimeter, Area, and Volume
EUM3.02: : determine an approximate value for π (pi) by investigating the relationship between the circumference and the diameter of a circle, using concrete materials to obtain measurements;
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
EUM3.03: : validate the formula for the circumference of a circle by comparing measurements of the circumference to the calculations, using the formula C = π d;
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
EUM3.04: : solve authentic problems requiring the calculation of the circumference of a circle;
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
EUM3.08: : validate the formula for the area of a circle by comparing approximate measurements of the area to the calculations, using the formula A = πr² (e.g., measure the area and radius of several circles, using concrete materials);
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
EUM3.09: : construct reasonably accurate diagrams of the angles 180°, 90°, 45°, 30°, and 60°, by dividing a given circle into the appropriate number of parts (e.g., to construct an angle of 45°, divide a given circle into eight equal parts);
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
EUM3.11: : establish that the volume of a cylinder is found by multiplying the area of its base by its height by comparing the structure of a prism to that of a cylinder (e.g., the top and bottom are identical and the sides are perpendicular to the top and bottom);
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
EUM3.12: : solve problems drawn from everyday situations involving the perimeters and the areas of circles and rectangles, and the volumes of cylinders and rectangular prisms.
Area of Parallelograms
Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
EPRV: : Extending Understanding of Proportional Reasoning
EPRV.01: : solve problems drawn from everyday situations, demonstrating skill and understanding in the use of fractions, percentages, ratios, and rates;
3.1.1: : Applying Fractions, Percent, Ratio, and Rate in Solving Problems
EPR1.07: : write ratios describing relationships in the school environment (e.g., the ratio of silver cars to white cars in the parking lot today is 7:15);
Beam to Moon (Ratios and Proportions) - Metric
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
EPR1.09: : solve problems using proportions (e.g., In making punch, the ratio of fruit juice to water is 1:3. How much water should be added if you have 3 litres of fruit juice?);
Beam to Moon (Ratios and Proportions) - Metric
Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview
Direct and Inverse Variation
Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions. 5 Minute Preview
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake. 5 Minute Preview
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
EPRV.02: : communicate information drawn from a variety of sources;
3.2.1: : Communicating Information
EPR2.02: : construct a variety of graphs (straight line, bar, circle), with and without the use of technology, to assist in identifying patterns in data or drawing conclusions from data;
Stem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview
EPRV.03: : use literacy skills (reading, writing, listening, and speaking) to extend understanding of proportional reasoning.
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
Correlation last revised: 9/16/2020
About STEM Cases
Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
STEM Cases take between 30-90 minutes for students to complete, depending on the case.
Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
Multiple grade-appropriate versions, or levels, exist for each STEM Case.
Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
How Free Gizmos Work
Start teaching with 20-40 Free Gizmos. See the full list.
Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
Free Gizmos change each semester. The new collection will be available January 1 and July 1.
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