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- Mathematics: 9th Grade
Ontario - Mathematics: 9th Grade
ON--Locally Developed Compulsory Credit Courses | Adopted: 2005
DMSV: : Developing and Consolidating Money Sense
DMSV.01: : interpret, write, and round decimal numbers with understanding in everyday money situations;
1.1.1: : Understanding and Using Decimals
DMS1.05: : interpret numerical information drawn from the media or through conversation and explain its significance, using familiar references (e.g., I read in the newspaper that an athlete earned $250 000 last year. How many hours would you need to work to earn that much money?);
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 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
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
Real-Time Histogram
Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected. 5 Minute Preview
DCMV: : Developing and Consolidating Concepts in Measurement
DCMV.01: : estimate and measure length, capacity, and mass, in order to consolidate understanding of the metric system;
2.1.1: : Understanding and Using the Metric System
DCM1.08: : estimate and use measurements of length, capacity, and mass in everyday applications (e.g., the distance from the school to the skating rink is about 1 km; the cups in the cafeteria hold about 350 mL; one protein bar has a mass of about 85 g).
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
DCMV.03: : solve problems, carry out investigations, estimate, and measure, using metric units, to consolidate understanding of perimeter, area, and volume
2.3.1: : Understanding and Applying Perimeter, Area, and Volume
DCM3.01: : explore and describe situations from everyday life and the workplace that require calculation or measurement of perimeter (e.g., fencing, wall paper borders, the baseboard around a room, the distance around a track or a baseball diamond);
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
DCM3.02: : estimate, measure, and calculate perimeters drawn from applications in everyday life and the workplace;
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
DCM3.04: : explore and describe situations from everyday life and the workplace that require calculating and measuring area (e.g., buying wallpaper, floor tiles, sod, patio slabs);
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
DCM3.05: : investigate the areas of a variety of rectangles and triangles, using concrete materials (e.g., square tiles, interlocking cubes, rectangular and triangular pattern blocks, triangle models, grid paper);
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
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
DCM3.07: : predict and explain, from experiences involving concrete materials, that the area of any rectangle can be found by multiplying its length by its width;
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 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
DCM3.08: : estimate and calculate the areas of rectangles and triangles, drawn from applications in everyday life and the workplace;
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
DCM3.09: : estimate and calculate the areas of regions that can be broken into rectangles (e.g., L-shaped floor plan, a garden, a roof);
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
DCM3.10: : explore and describe situations from everyday life and the workplace that require calculation or measurement of volume (e.g., the size of a package, the amount of soil to purchase, the volume of air in a room, amount of liquid medication);
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
DCM3.12: : predict and explain, from investigations involving the building of prisms, that the volume of a prism is given by multiplying the area of its base by its height;
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
DCM3.13: : estimate and calculate the volumes of rectangular prisms drawn from applications in everyday life and the workplace;
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
DCM3.14: : select the most appropriate standard unit to measure the perimeter, area, or volume of a figure (e.g., use centimetres squared or cm² to measure the area of a book cover, but use metres squared or m² to measure the area of a wall);
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
DCM3.16: : solve problems involving perimeter, area, and volume in applications drawn from everyday situations.
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
DPRV: : Developing Concepts in Proportional Reasoning
DPRV.01: : determine relationships among fractions, percentages, ratios, and rates by constructing diagrams, building models, and estimating measurements;
3.1.1: : Constructing Understanding of Fractions, Percentages, Ratios, and Rates
DPR1.11: : identify and use ratios, including equivalent ratios, to express the relationships among quantities represented by models and diagrams;
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
DPR1.12: : explore and describe the use of ratios from their personal experiences (e.g., ratio of ingredients in a recipe, bicycle gear ratios, the ratio of red cars to blue cars in the school parking lot is 12:10 or 6:5);
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
DPR1.13: : explore and identify rates drawn from their experiences and the units used in them (e.g., the speed limit for an automobile in the city is 50 km/h);
Household Energy Usage
Explore the energy used by many household appliances, such as television sets, hair dryers, lights, computers, etc. Make estimates for how long each item is used on a daily basis to get an estimate for the total power consumed during a day, a week, a month, and a year, and how that relates to consumer costs and environmental impact. 5 Minute Preview
DPRV.02: : solve problems drawn from everyday situations involving percent, ratio, rate, and fractions;
3.2.1: : Solving Problems
DPR2.02: : solve simple problems using equivalent ratios (e.g., recipes, scale diagrams);
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
DPR2.04: : calculate and compare the unit costs of items found in everyday situations (e.g., compare the cost of one bottle of water bought from a vending machine versus the cost of one bottle from a case of 24);
Household Energy Usage
Explore the energy used by many household appliances, such as television sets, hair dryers, lights, computers, etc. Make estimates for how long each item is used on a daily basis to get an estimate for the total power consumed during a day, a week, a month, and a year, and how that relates to consumer costs and environmental impact. 5 Minute Preview
DPRV.03: : communicate information about proportional reasoning;
3.3.1: : Communicating Information about Proportional Reasoning
DPR3.01: : verbalize their observations and reflections regarding proportional reasoning and ask questions to clarify their understanding (e.g., talk about their own and other students’ solutions to problems);
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
DPR3.02: : explain their reasoning used in problem solving and in judging reasonableness;
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
DPR3.03: : communicate, orally and in writing, the solutions to proportional reasoning problems and the results of investigations, using appropriate terminology, symbols, and form.
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.
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