# 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.