Using Student Activities
Grade 6 - Prime Time
The Factor Game
How To Use (video) | Launch the Factor Game
Suggested Uses
Problem 1.1 Launch.
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about factors and multiples coming into the unit.
Purpose
Identifying proper factors of whole numbers
Description
The game is played on a board that contains the positive integers 1-30. Players take turns choosing a whole number. The first player picks a number and the other player selects all the proper factors of that number. Once either player has selected a number, that number is unavailable for future turns. The game ends when there are no numbers with proper factors left on the board. Each player adds the selected proper factors that he/she has selected. The person with the greater total wins the game.
Game options include extending the game board to contain the whole numbers 1-49 or 1-100. A player can compete against the computer or another player.
Related Links
Factor Game on NCTM Illuminations - This version allows you to change the number of rows and columns. The existing DASH applet is only for grids of 30, 49 or 100..
The Product Game
How to Use (video) | Launch the Product Game
Suggested Uses
Problem 1.3 Launch
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about factors and multiples coming into the unit.
Purpose
Identifying proper factors of whole numbers
Description
A two-player game in which players take turns choosing a pair of whole numbers from 1-9. For each product they form, they place a chip on a board, on the appropriate number. First player to have four chips in a row wins.
Game options include changing the factors in play or changing the number in a row to win.
Related Links
Product of Game on NCTM Illuminations - This version provides an option to play against a computer.
The Locker Problem
How to Use (video) | Launch the Locker Problem
Suggested Uses
Problem 3.4 Launch
Purpose
Connecting ideas about factors, multiples, and prime numbers
Description
Students explore number patterns by opening and closing a row of lockers numbered 1-1000. The first student opens every locker; the second student starts with the second locker and closes every other locker; the third student starts with the third locker and changes the state of that locker and every other third locker; etc. After all the students have gone through, which lockers remain open?
Grade 6 - Comparing Bits and Pieces
Target Game
How to Use (video) | Launch the Target Game
Suggested Uses
Problem 1.3 Summarize; Problem 3.4 Summarize
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about fractions and decimals coming into the unit.
Purpose
Connecting equivalent fractions and equivalent decimals; comparing fractions and decimals; locating fractions and decimals on a number line
Description
Players take turns to roll a die and use the values on the die to form fractions (numerators and denominators); one roll to form a numerator and one for a denominator. After each player has formed five fractions, the player who has the fraction closest to the given "target fraction" wins.
Game options include playing with fractions or decimals.
Grade 6 - Let's Be Rational
Fraction Game
How To (video) | Launch the Fraction Game
Suggested Uses
Problem 1.3 Summarize
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about addition and subtraction of fractions at the start of
the unit.
Purpose
Developing strategies for adding and subtracting fractions less than 1
Description
Players are given seven number lines with different sub-units (halves, thirds, quarters, etc.). Both players use the same number lines. After drawing a card that contains a fraction, a player can move his/her slider to a point on a number line, provided the distance is less than or equal to the fraction on the card. Each player must get his/her sliders to the end of each number line. First player to get all seven sliders to the right side of the number lines wins.
Related Links
Fraction Game on NCTM Illuminations - This is for 1 player only.
Grade 6 - Covering and Surrounding
Areas and Perimeters of Shapes and Images - Rectangular & Non-Rectangular Shapes
Launch the Areas and Perimeters of Shapes and Images
Suggested Uses
Problem 1.1 Explore or Summarize
Note: This can also be used as review in Grade 7: Filling and Wrapping
Purpose
Creating shapes with a given area and perimeter; finding the area and perimeter of rectangular and non-rectangular shapes
Description
Students create shapes on virtual graph paper. They use the number and size of grid squares to estimate areas and perimeters of their shapes.
Areas and Perimeters of Shapes and Images - Triangles
Launch the Areas and Perimeters of Shapes and Images
Suggested Uses
Problem 2.1; Problem; 2.2; Problem 2.3; Problem 2.4
Note: This can also be used as review in Grade 7: Filling and Wrapping
Purpose
Finding areas and perimeters of triangles
Description
Students create shapes on virtual graph paper. They use the number and size of grid squares to estimate areas and perimeters of their shapes.
Areas and Perimeters of Shapes and Images - Parallelograms
Launch the Areas and Perimeters of Shapes and Images
Suggested Uses
Problem 3.1; Problem; Problem 3.2; Problem3.3; Problem 3.4
Note: This can also be used as review in Grade 7: Filling and Wrapping
Purpose
Finding areas and perimeters of parallelograms
Description
Students create shapes on virtual graph paper and then use the number and size of grid squares to estimate areas and perimeters of their shapes.
Virtual Box
How to (video) | Launch Virtual Box
Suggested Uses
Problem 4.1; Problem 4.2; Problem 4.3
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about know about volume and prisms prior to this Investigation.
It can also be used as review in Grade 7: Filling and Wrapping
Purpose
Finding the surface area and volume of rectangular prisms
Description
Students create boxes of various dimensions, unfold the boxes to create nets, and "fill" the boxes with cubes to calculate volume. This activity facilitates understanding volume of prisms as "filling the base" and looking at the "number of stacks" to fill a prism.
Grade 6 - Decimal Ops
Target Game
How to Use (video) | Launch the Target Game
Suggested Uses
Use review anytime in Decimal Operations unit
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about fractions and decimals coming into the unit.
Purpose
Exploring equivalent fractions and decimals; comparing fractions and decimals; locating fractions and decimals on a number line
Description
Players roll die and form fractions (numerators and denominators) using the values that appear on the die. After each player has filled all ten slots, the player who has the closest fraction to the given "target fraction" wins.
Game options include playing with fractions or decimals.
Grade 6 - Variables and Patterns
Climbing Monkeys
How To Use (video) | Launch Climbing Monkeys
Suggested Uses
Problem 3.3 Summarize
Note: This can also be used in Grade 7: Moving Straight Ahead and Grade 8: Thinking with Mathematical Models.
Purpose
Exploring patterns of change in equations and graphs; modeling the climb or decline of the monkeys using two linear algebraic equations
Description
Students set the "climbing options" for two monkeys, and watch the monkeys ascend or descend palm trees. The vertical heights of the monkeys are graphed on an associated grid. Monkeys can climb up or down at different speeds, and start from different heights.
Grade 7 - Shapes and Designs
Bee Dance Activity
How To Use (video) | Launch Bee Dance Activity
Suggested Uses
Problem 1.3 Summarize
Purpose
Estimating the measure of an angle
Description
Students estimate the angle the bee must travel to get to the flower, relative to the sun. Students press OK to check their answer and if needed, enter new guesses until it is correct.
Tessellations
How To: Tessellations Launch Tessellations
Suggested Uses
Problem 2.3 Explore
Note: This can also be used in Grade 7: Stretching and Shrinking and Grade 8: Butterflies, Pinwheels, and Wallpaper
Purpose
Exploring properties of symmetry, repetition, and tiling. Construct your own tessellations
Description
Students experiment with different regular polygons, or combinations of polygons, to see which figures will tile a plane. Tessellations can be used to explore the relationship between tessellations and reptiles like those shown in the Student Book for Stretching and Shrinking pages 50 and 51.
Related Links
Tessellations on NCTM Illuminations
Virtual Polystrips
Suggested Uses
Problem 3.1 Explore; Problem 3.3 Explore
Purpose
Building the triangles described in 3.1 and the quadrilaterals in 3.3; exploring properties of polygons; exploring the relationships between side lengths of triangles and quadrilaterals; measuring length and area and angle measures
Description
Students construct polygons using strips of different lengths. This tool allows them to measure angles and lengths, attach polystrips to each other, and rotate polystrips freely.
Quadrilateral Game
Suggested Uses
Problem 3.5 Launch, Explore, and Summarize
Purpose
Creating quadrilaterals satisfying certain properties, using what you know about side, angle, and symmetry properties of quadrilaterals
Description
Player 1 creates a quadrilateral that matches a given description. Player 2 then creates a quadrilateral that matches a new description, moving as few corners of the existing quadrilateral as possible. A player scores one point for every corner moved. The player with the lowest score after five turns wins.
The game can be introduced and initially played with two partners on each team (pair vs. pair). This strategy should increase the use of vocabulary and improve understanding of the game. When partners have played partners at least one time, students can play each other one-on-one.
Optional use: Assign students to play a family member for homework after experiencing the game in class.
Grade 7 - Accentuate the Negative
Integer Product Game
Suggested Uses
Problem 3.4 Launch, Explore, and Summarize
Note: This can be used as review or additional practice as needed.
Purpose
Developing fluency with multiplication and division of integers
Description
A two-player game in which players take turns choosing a pair of integers numbers from a pre-determined list of 12 choices, ranging from -99 to 99. For each product they form, they place a chip on a board, on the appropriate number. A student has to think about the consequences of choosing a number on the factors list; how to position himself or herself to make a mark while thinking about how his/her opponent(s) might be able to benefit from the factor choice. First player to have four chips in a row wins.
Suggestions for using the activity in the Launch, Explore, or Summarize are as follows:
- Launch: Play one game with class so that everyone understands the rules.
- Explore: This is a two-person game. Have students pair up and play the game a few times. Some teachers find it productive to let teams of two play against each other. This allows the teammates to share and discuss strategies.
- Summarize: Discuss the strategies students used.
Grade 7 - Stretching and Shrinking
Mug Wumps
Suggested Uses
Problem 1.2 Summarize; Problem 2.2 Summarize; Problem 2.3 Launch, Explore, and Summarize
Note: This can be used with various ACE questions or as review or additional practice.
Purpose
Making similar and non-similar shapes using a coordinate system; investigating the effects that algebraic rules have on the shape and location of a figure on a coordinate grid; comparing properties of similar rectangles and triangles
Description
Students explore the properties of different polygons, including members of the "Wump" family. This tool allows them to measure lengths, angles, perimeters, areas, and slopes. Students can create their own polygons and verify that they belong to a family of similar figures, or not.
Grade 7 - Comparing and Scaling
Paper Pool
Suggested Uses
Unit Project
Purpose
Investigating the pattern of bounces a pool ball makes its way around pool tables of various dimensions
Description
Students shoot a ball on a pool table and predict a) in which pocket the ball will stop and b) how many hits are needed. They can vary the dimensions of the table to begin to see patterns and relationships that will inform their predictions. Students gather and organize data, search for patterns, recognize similar rectangles, and use the simplest ratio to predict the stopping pocket and number of hits.
Related Links
- NCTM Illuminations applet
- Related Video (Uses Fractions)
- Additional Video (Better for a Geometry Unit)
Grade 7 - Moving Straight Ahead
Climbing Monkeys
How To Use (video) | Launch Climbing Monkeys
Suggested Uses
Problem 3.5 Summarize -Check for Understanding; Problem 4.3 Launch
Note: This activity can be used in Problem 3.5: Identify the point of intersection
of two lines, as a Check for Understanding. In Problem 4.3: Compare the slopes of
lines, students can use this activity to compare the graphs of monkeys who climb at
the same rate but begin at different heights. Students can then make conjectures about
similarities and differences in the equations representing the monkeys’ heights.
This is also suggested for Grade 6: Variables and Patterns and Grade 8: Thinking With Mathematical Models.
Purpose
Investigating the relationship between two variables; using graphic methods to find solutions to a system of linear equations by finding a point of intersection for two lines; exploring rates of change and finding the slope of a line; exploring the role of the y-intercept in a linear relationship
Description
Students set the "climbing options" for two monkeys, and watch the monkeys ascend or descend palm trees. The vertical heights of the monkeys are graphed on an associated grid. Monkeys can climb up or down, at different speeds, and start from different heights. The options for assigning y-intercepts and rates are limited to positive integer values.
Grade 7 - Filling and Wrapping
Virtual Box
How to (video) | Launch Virtual Box
Suggested Uses
Problem 1.1 Launch, Explore, and Summarize; Problem 1.4 Explore
Note: This activity is particularly helpful to use with Problem 1.1.C: Calculate the number of layers and the total number of shipping containers, and to calculate the total boxes in Problem 1.4.D: Help students determine the surface area and volume for the first three compost boxes. It can also be used with Covering and Surrounding in 6th grade.
Purpose
Finding the surface area and volume of rectangular prisms
Description
Students create boxes of various dimensions, unfold the boxes to create nets, and "fill" their boxes with cubes to calculate volume. This activity facilitates understanding volume of prisms as "filling the base" and looking at the "number of stacks" to fill a prism.
Areas and Perimeters of Shapes and Images
Launch Areas and Perimeters of Shapes and Images
Suggested Uses
Problem 3.2 Explore
Note: This activity can be used during the Explore phase of Problem 3.2 to estimate area
of the circles. It can also be used in Grade 6: Covering and Surrounding.
Purpose
Finding the surface area and volume of rectangular prisms
Description
Students create shapes on virtual graph paper and then use the number and size of grid squares to estimate areas and perimeters of their shapes.
Virtual Cylinder
Suggested Uses
Problem 4.2 Summarize
This can be used in Problem 3.2, during the Explore phase, to estimate the area of
the circles.
Purpose
Exploring the properties of cylinders; estimating volume and surface area of cylinders
Description
Students create cylinders of various heights and diameters. They can then use unit cubes, or circular "slices" to fill their cylinders. These features allow students to enter estimates of the actual volume of their cylinder, which the program evaluates as "not very close", "pretty close", etc. Eventually students hypothesize about the volume of a cylinder based on its height and diameter. Students visualize the volume of a cylinder as stacks or layers of the number of unit cubes that sit on the base.
Pouring and Filling
How to Use (video) | Launch Pouring and Filling
Suggested Uses
Problem 4.4 Summarize; Problem 4.5 Explore or Summarize
Note: This activity can be used during the Pouring and Filling for any of the following
reasons in Problem 4.4: 1) to Summarize and verify the relationships that students
discover after doing the experiments; 2) for students who were absent to make up their
work; and/or 3) as an extension that can lead into the ACE Exercises about the relationship
between volumes of pyramids and prisms. Students can use this activity to check their
answers to Problem 4.5. This can also be used in Grade 8: Say It With Symbols.
Purpose
Comparing and filling cylinders, cones, and spheres; comparing and filling a cube with a square pyramid
Description
Students explore the relative volumes of spheres, cylinders, prisms, pyramids, and cones. Each shape is virtually "filled" with water, and then "emptied" into one of the other shapes. For example, a student might fill a sphere, and empty its contents into a cone. Students may then hypothesize about the formula for the volume of a cone as a proportion of the volume of a sphere.
Grade 7 - Review of Fraction and Decimal Equivalence
Target Game
How to Use (video) | Launch Target Game
Suggested Uses
Review of fraction and decimal equivalence
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about fractions and decimals coming into the unit. This can
also be used in Grade 6: Comparing Bits and Pieces and Decimal Ops.
Purpose
Exploring equivalent fractions and decimals; comparing fractions; comparing decimals; locating fractions and decimals on the number line
Description
Players roll die and form fractions (numerators and denominators) using the values that appear on the die. After each player has filled all ten slots, the player who has the closest fraction to the given "target fraction" wins.
Game options include playing with fractions or decimals.
Grade 8 - Thinking with Mathematical Models
Virtual Bridge Experiment
How To Use (video) | Launch Virtual Bridge Experiment
Suggested Uses
Problem 1.1 Explore; Problem 1.2 Explore
Note: Students can use the Virtual Bridge Experiment to simulate the experiment.
Purpose
Exploring relationships between two variables, using both a linear and non-linear model; making predictions based on a mathematical model
Description
Students create a "bridge" of selected thickness and length. The bridge supports a cup that is filled with pennies, until the bridge collapses. Based on multiple experiments, students hypothesize a relationship for the number of pennies needed to break a bridge based on thickness or length of the bridge.
Climbing Monkeys
How To Use (video) | Launch Climbing Monkeys
Suggested Uses
Problem 2.2; Problem 2.3; Problem 2.5 Explore
Note: Students can use Climbing Monkeys to explore the concepts of slope, y-intercept,
and the equation of a line and explore how the point of intersection of the two models
relates to the context that the models represent. It can also be used in Grade 6:
Variables and Patterns and Grade 7: Moving Straight Ahead
Purpose
Investigating the relationship between two variables; using graphic methods to find solutions to a system of linear equations by finding a point of intersection for two lines; exploring rates of change and finding the slope of a line; exploring the role of the y-intercept in a linear relationship
Description
Students set the "climbing options" for two monkeys, and watch the monkeys ascend or descend palm trees. The vertical heights of the monkeys are graphed on an associated grid. Monkeys can climb up or down, at different speeds, and start from different heights.
Grade 8 - Looking for Pythagoras
Interactive Pythagoras
How To Use (video) | Launch Interactive Pythagoras
Suggested Uses
Problem 3.1 Summarize; Problem 3.2 Launch
Purpose
Examining the relationships between the lengths of the sides of a right triangle and the areas of squares built on those same sides
Description
In this visual demonstration of the Pythagorean Theorem, students change the lengths of the sides of a right triangle. This in turn changes the dimensions of the three squares adjacent to the sides of the triangle. Using the "shearing" technique, students observe that the squares on the legs of the triangle will always occupy the same area as the square on the hypotenuse of the triangle.
Related Links
Activity on NCTM Illuminations
Painted Cubes
Suggested Uses
Problem 2.4 Launch
Note: This activity could also be used in Looking for Pythagoras, Problem 2.4 during the Launch to have students find the perfect cube numbers before
discussing cube root.
Purpose
Exploring linear, quadratic, and cubic relationships
Description
Students build a rectangular prism out of unit cubes and then color the faces of their prism using a palate of colors. Rotating the prism allows them to paint sides that are initially hidden. An "expand" option allows them to "blow up" their prism to see the interior unit cubes. An "inspect" tool counts the number of cubes with 0, 1, 2, or 3 painted faces.
Grade 8 - Frogs, Fleas, and Painted Cubes
Painted Cubes
Suggested Uses
Problem 4.3 Explore
Note: This activity can also be used in Looking for Pythagoras, Problem 2.4 in the Launch
to find perfect cube numbers before discussing cube root.
Purpose
Exploring linear, quadratic, and cubic relationships
Description
Students build a rectangular prism out of unit cubes and then color the faces of their prism using a palate of colors. Rotating the prism allows them to paint sides that are initially hidden. An "expand" option allows them to "blow up" their prism to see the interior unit cubes. An "inspect" tool counts the number of cubes with 0, 1, 2, or 3 painted faces.
Grade 8 - Butterflies, Pinwheels, and Wallpaper
Transformations
Suggested Uses
Problem 1.1; Problem 1.2; Problem 1.3; Problem 3.1; Problem 3.2; Problem 3.3; Problem
3.4; Problem 3.5; Problem 4.1; Problem 4.3
Note: This can be used for the Launch, Explore or Summarize for all these problems. This
activity may help to reduce the amount of class time reserved for drawing designs.
Purpose
Exploring and describing different kinds of symmetry; using symmetry transformations
Description
Students create geometric figures, and experiment with different transformations, such as reflections, rotations, and translations. They can create copies of their figure and alter the scale factor. Tools that calculate perimeter, angles, and area allow students to see which properties are conserved under which transformations.
Note: The default setting of this activity includes a grid and axes, but there is the option to remove them.
Tessellations
How To: Tessellations | Launch Tessellations
Suggested Uses
Review of tessellations and symmetry
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about tessellations and symmetries coming into the unit. It
can also be used in Grade 7: Shapes and Designs.
Purpose
Exploring properties of symmetry, repetition, and tiling; constructing tessellations
Description
Students create symmetric design and describe all the possible reflection, rotation, or translation symmetries they see in their figure.
Hubcap Maker
Suggested Uses
Problem 1.1; Problem1.2 Launch or Explore
Note: This can also be used as a review, an additional practice, or an assessment of what
students already know about reflectional and rotational symmetry coming into the unit.
Purpose
Exploring reflectional and rotational symmetry. Identifying lines of symmetry, and working with basic design elements.
Description
Students create decorative hubcap patterns, starting with simple geometric shapes, and using various tools to reflect, rotate, and copy the shape. They can create multiple copies of a shape at specified axes of rotation, such as 6 copies spaced 60 degrees apart, etc.
Grade 8 - Say It With Symbols
Pouring & Filling
How To Use (video) | Launch Pouring & Filling
Suggested Uses
Problems 2.3 Launch and Explore
Note: This can also be used in Grade 7: Filling and Wrapping
Purpose
Exploring the relationships between the volume formulas for spheres, cones, prisms, and cylinders
Description
Students explore the relative volumes of spheres, cylinders, prisms, pyramids, and cones. Each shape is virtually "filled" with water, and then "emptied" into one of the other shapes. For example, a student might fill a sphere, and empty its contents into a cone. Students hypothesize about the formula for the volume of a cone as a proportion of the volume of a sphere. Students also show why one or more symbolic statements for a relationship are equivalent.