Number and Operations

In grades 6 – 8, all students should:

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meaning of operations and how they relate to one another
• Compute fluently and make reasonable estimates

Concept

Description

Produced by

Fractions, Decimals and Percents

Size-O-Rama

Use fractions, decimals, and percents to determine an unknown height.

Determine an unknown height using the decimal value of equivalent ratios.

Sunnyside Up

Use fractions to size up a biscuit recipe.

Ratios and Proportions

Din-O-Rama

Resize a figure to fit the scale of a diorama.

Use the proportional relationship between similar triangles to determine unknown heights.

Mural Math

Explore what happens to area when you scale up a painting proportionally.

House of Scales

Calculate the dimensions of a house that has been scaled up by a factor of 10.

Sunnyside Up

Scale up menu items to feed a crowd at a family reunion.

Discover the relationship between an object’s distance from a light source and the size of its shadow.

Explore the proportional relationship between the length of musical pipes and their frequency.

At the Track

Learn about the proportional relationships among time, distance, and speed.

London

Write and solve proportions when ratios are given as fractions, decimals, and percents.

Tokyo

Solve problems by using proportions.

Fractions, Decimals and Percents

Photo Booth

Determine the proportional relationship between battery charge and the number of photos one can take.

Bumper Cars

Control the mass and velocity of a bumper car.

Rio de Janeiro

Write and compare ratios using fractions and decimals.

Ratios and Proportions

Photo Booth– Rechargeable Batteries

Determine the proportional relationship between battery charge and the number of photos one can take.

Estimating and Predicting

Bumper Cars– Storing and Using Energy in a Battery

Control the mass and velocity of a bumper car.

Selecting Appropriate method of computation and reasonable of result

Drag Racing - Horsepower

Calculate horsepower and explore accelerating from 0 to 60 mph.

Computing fluently

Roller Coaster - The Inclined Plane

Determine the amount of force required to pull roller coasters up inclined planes.

Parachute Drop - The Pulley

Explore and calculate force using different weights of people and different numbers of pulleys.

Seesaw – The Lever

Explore different weights and positions needed to balance a seesaw.

Ring the Bell – Acceleration

Explore the force that is necessary to “ring the bell.”

Roller Coaster – Scale Factor

Explore scale factors of roller coasters, dinosaurs and statues.

Determining Unit Rate

Photo Booth– Rechargeable Batteries

Determine the proportional relationship between battery charge and the number of photos one can take.

Bumper Cars– Storing and Using Energy in a Battery

Control the mass and velocity of a bumper car.

Barcelona

Determine unit rates.

Converting Units of measurement between metric and customary

Bumper Cars– Storing and Using Energy in a Battery

Control the mass and velocity of a bumper car.

Parachute Drop - The Pulley

Explore and calculate force using different weights of people and different numbers of pulleys.

Roller Coaster – Scale Factor

Explore scale factor of roller coasters, dinosaurs and statues.

Algebra

In grades 6 – 8, all students should:

• Understand patterns, relationships, and functions
• Represent and analyze mathematical situations and structures using algebraic symbols
• Use mathematical models to represent and understand quantitative relationships
• Analyze change in various contexts

Concept

Description

Produced by

Different forms of representation for a relationship

Sunnyside Up

Observe how the relationship of radius vs. area of circle is represented in a graph.

Enter data in a table and see how it translates into a graph.

At the Track

Compare the graphical representations of inverse and direct proportions.

Modeling problems with graphs, tables, and equations

House of Scales

Complete a table comparing the dimensions of a house those of a larger-scale version.

Sunnyside Up

Complete a table with the ingredients for a scaled-up recipe.

Complete a table with measurements of shadows at different distances from a movie projector.

Musical Scales

Complete a table that demonstrates the relationship between the length of musical pipes and their frequency.

At the Track

Complete a table that illustrates how distance, time, and speed are related.

Analyze change

Sunnyside Up

Use a graph to determine how big a skillet needs to be to cook 108 pieces of chicken.

At the Track

Answer questions about rate based on graphs of distance vs. speed and time vs. speed.

Comparing, graphing and interpreting data

Photo Booth– Rechargeable Batteries

Determine the proportional relationship between battery charge and the number of photos one can take.

Modeling problems with graphs, tables, and equations

Bumper Cars– Storing and Using Energy in a Battery

Control the mass and velocity of a bumper car.

Drag Racing – Horsepower

Calculate horsepower and explore accelerating from 0 to 60 mph.

Roller Coaster - The Inclined Plane

Determine the amount of force required to pull roller coasters up inclined planes.

Parachute Drop - The Pulley

Explore and calculate force using different weights of people and different numbers of pulleys.

Seesaw – The Lever

Explore different weights and positions needed to balance a seesaw.

Ring the Bell – Acceleration

Explore the force that is necessary to “ring the bell.”

Roller Coaster – Scale Factor

Explore scale factors of roller coasters, dinosaurs and statues.

Geometry

In grades 6 – 8, all students should:

• Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
• Specify locations and describe spatial relationships using coordinate geometry and other representational systems
• Apply transformations and use symmetry to analyze mathematical situations
• Use visualization, spatial reasoning, and geometric modeling to solve problems

Concept

Description

Produced by

Transformations – Reflections

Bring Your Own Food

Place picnic tables to reflect a given arrangement.

Transformations – Rotations

Who’s Hungry

Place, size, and rotate a shape to represent a snack bar in a park.

Get Physically Fit

Place, reflect, and rotate objects in an obstacle course.

Pythagorean Theorem

Light the Way

Find the distance between two light posts.

Alley Oops

Calculate the amount of material needed to cover a ramp.

Access for All

Calculate the amount of material needed to cover a ramp and install rails along the sides.

Pythagorean Theorem

Roller Coaster - The Inclined Plane

Determine the amount of force required to pull roller coasters up inclined planes.

Transformations - Translations

Alley Oops

Determine the coordinates needed to move a skateboarder along a rail.

Get Physically Fit

Place and translate objects in an obstacle course.

E-luminate

Describe the translations needed to move a person on a coordinate plane.

Two- and three-dimensional geometric shapes

Use similarity to help determine an unknown height.

Mural Math

Explore what happens to area when the dimensions of similar rectangles are increased proportionally.

House of Scales

Observe what happens to volume when three-dimensional objects are scaled up.

Sunnyside Up

Explore what happens to the area of a circle when its radius is increased.

Spatial relationships using coordinate geometry

Sunnyside Up

Observe how the relationship between a circle’s radius and its area is represented graphically.

Applying geometry to areas outside mathematics classroom

Mural Math

See how proportional reasoning is used to create large-scale murals.

Measurement

In grades 6 – 8, all students should:

• Understand measurable attributes of objects and the units, systems, and processes of measurement
• Apply appropriate techniques, tools, and formulas to determine measurements

Concept

Description

Produced by

Proportional Reasoning

Ahoy Matey

Place and size a pond in a park.

Alley Oops

Place and size a skateboard ramp in a park.

Pentagonal Plot

Place and size a garden in an environmental center.

3 R’s

Place and size a gazebo in an environmental center.

Musical Scales

Discover the proportional relationship between the length of a musical pipe and its frequency or pitch.

Size-O-Rama

Measure an unknown height using information about a known height.

Din-O-Rama

Scale a figure for placement in a diorama.

At the Track

Explore the proportional relationships among speed, distance, and time.

Calculate an unknown height using shadows and similar triangles.

House of Scales

Determine the dimensions, area, and volume of a house using a 1:10 scale.

Mural Math

Determine how much more paint is needed when the length and width of a painting are doubled or tripled.

Explore the relationship between the size of an object’s shadow and its distance from a light source.

Sunnyside Up

Scale up recipes for a family reunion.

Sunnyside Up

Scale up a skillet to cook chicken for a crowd.

Applying the Process of Measurement

Roller Coaster – Scale Factor

Explore scale factors of roller coasters, dinosaurs and statues.

Scale Factors

Paris

Measure distances on a map and calculate the actual distances.

Volume of a Cylinder

Ahoy Matey

Calculate the volume of a pond and the amount of water needed to fill it.

Calculate the volume of a pond and the amount of water needed to fill it.

Area of a Circle

Calculate the number of goldfish that can be placed in a pond.

Sunnyside Up

See how increasing the radius of a circle affects its area.

Perimeter and Circumference

Slam Dunk

Calculate the number of cans of spray paint needed to paint the lines on a basketball court.

Maryland Public Television

Perimeter and Area

Tokyo

Solve problems using perimeters and areas of rectangles.

Area of a Composite Figure

Safety First

Find areas of composite figures in order to cover areas in a park with rubberized mulch.

Pentagonal Plot

Find area of composite figure in order to cover it with topsoil.

3 R’s

Find area of composite figure in order to cover it flooring.

Rates and derived measurements

At the Track

Calculate speed in mph based on distance traveled in a set time or time taken to travel a set distance.

Solving Problems Using Velocity and Mass

Bumper Cars– Storing and Using Energy in a Battery

Control the mass and velocity of a bumper car.

Data and Probability

In grades 6 – 8, all students should:

• Understand and apply basic concepts of probability

Concept

Description

Produced by

Using proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations

Photo Booth– Rechargeable Batteries

Determine the proportional relationship between battery charge and the number of photos one can take.

Bumper Cars– Storing and Using Energy in a Battery

Control the mass and velocity of a bumper car.

Drag Racing – Horsepower

Calculate horsepower and explore accelerating from 0 to 60 mph.

Roller Coaster - The Inclined Plane

Determine the amount of force required to pull roller coasters up inclined planes.

Parachute Drop - The Pulley

Explore and calculate force using different weights of people and different numbers of pulleys.

Seesaw – The Lever

Explore different weights and positions needed to balance a seesaw.

Ring the Bell – Acceleration

Explore the force that is necessary to “ring the bell.”

Roller Coaster – Scale Factor

Explore scale factors of roller coasters, dinosaurs and statues.