Kindergarten Greater Than, Less Than, Equal To More Less Parachute

Standard: K.CC.C.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to ten objects).

Game Description: Select a set of stacked objects that will be greater than, less than, or equal to a given set of stacked objects.

Test Drive -> Kindergarten -> Greater Than, Less Than, Equal to -> More Less Parachute -> Level 3 and Level 4

Suggested Puzzles:

Level 3

Level 4

Materials: Blocks, Number Lines (Can use a ruler if that helps students build it out to show the slant for or =)

Directions: Give students blocks. Project a puzzle from level 3. Ask students to use the blocks to show the number being represented in the puzzle. Have students determine if they need more or less blocks to get JiJi to parachute. Have students model possible solutions with the blocks.

Sample questions: • How tall is the green tower? How tall could you make the white tower? • How did you decide how many blocks to use to build the white tower? • How do you know that it is more? How do you know it is less? • Who built a different size tower?

What to look for: How does the student: • Figure out how many blocks are needed? (Do they match up the blocks? Do they count on or count all?) • Explain their solution. (Do they use language like “more than” or “less than”? Are they able to compare the

number of blocks they selected to the number of blocks given?)

Extensions:

• Give students a number line. Have them plot their blocks on the number line to “prove” their answers. • Draw a big number line on the board. Plot the given number with an “x”. Select 3-5 students to plot their

solutions on the number line. Compare the relationships between the given number and the students’ solutions. (Great opportunity to model mathematical language (ex. “2 more than,” “3 less than,” etc.) and establish relationships between numbers.)

Kindergarten Foundations of Place Value Ten Frame Counting Standard: K.CC.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Game Description: Decompose a number less than 20 into two parts. Record the decomposition using a visual equation. Where to find the game Test drive -> Foundations of Place Value -> Module 2 -> Ten Frame Counting -> Level 3 and 4 Suggested Puzzles:

Level 3

Level 4

Materials: Double Ten Frames, plastic chips or blocks, white boards and markers

Directions: Play level 1 of Ten Frame Counting to introduce students to the game. Have an informal discussion about what they notice happening in the puzzle. Give students Double Ten Frames and plastic chips or blocks. Project a puzzle from level 3. Have students model the ten frames with their blocks. Have them determine how many are needed to solve the puzzle. Have students share their solution with a neighbor. Select different students to share their solution with the class. Have them prove their solution by showing how they got their answer by modeling with any tools they used (blocks, plastic chips, paper, pencil, whiteboard, etc.) Discuss the different ways students solved the problem. Sample questions: • What do you notice in this game? • If the frame is full what do we know about the number of dots? • How do you see the dots in the frame on the right that helps you count them? • How do you determine the number needed at the bottom (in the grass)? What strategies are they using?

What to look for: How does the student: • Understand the problem represented in the puzzle? • Find the solution? (Does the student count on or count all?) • Explain how to solve the puzzle? (Does the student make 10?)

Extensions: • Give students a number line and have them model the problem from the ten-frame in the puzzle on the number

line.

First Grade Addition and Subtraction Situations with Unknowns Pie Monster Addition

Standard: 1.CC.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ___ - 3, 6 + 6 = ___.

Game Description: Use the model to solve addition problems. Includes missing addend. Test Drive -> 1st Grade -> Addition and Subtraction Situations with Unknowns -> Addition and Subtraction Relationships -> Pie Monster Addition-> Level 4 Suggested Puzzles:

Materials: Game mats, 2 color counters, paper and pencil, dry erase markers, whiteboards Directions: • Play level 1 of the Pie Monster Game to introduce students to the game. Have an informal discussion about

what they notice happening in the puzzle. • Make game mats, paper, white boards and 2 color counters available for students as math tools. Project a

puzzle from level 4. Have the students model the problem and solution using their math tools. Have students explain to a neighbor how their model represents the problem and solution. Select different students to share (look for different types of strategies) and discuss as a class.

Sample questions: • What is the question this puzzle is asking us to solve? • How did you solve the puzzle? • Explain how your model represents the puzzle. • Can you write an equation to represent this puzzle?

What to look for: How does the student: • Solve the puzzles (Are they thinking flexibly about addition and subtraction? Do they struggle with specific

problem types? (ex. result unknown, change unknown, start unknown)) • Are the students able to write an equation to represent the problem? (Great opportunity to connect the visual to

the symbolic and reinforce the meaning of equality as “same as.”) Extensions: • Show students a puzzle. Have them create a word problem from the puzzle. • Place students in pairs and give them a game mat. Have them take turns rolling a number cube (1-5). Each

student will select what he/she wants the number they rolled to represent and draw it on the game mat. (Ex. Student A rolls a 3 and draws three pies on the monster. Student B rolls a 5 and draws five pies on the conveyor belt). Once both students have drawn their pies on the game mat, they will work to solve the problem and represent it with an equation.

Second Grade Addition Subtraction Situations How Many More?

Standard: 2.CC.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 2.CC.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Game Description: Describe the difference between two whole numbers using models as well as the words less, greater, and equal. Test Drive > 2nd Grade > Addition and Subtraction Situations > How Many More?

Suggested puzzles:

Level 2 Level 1 puzzle instead

Level 3

Materials: Linking cubes, counting tiles, paper/pencil Directions: Students solve given puzzles using counting tiles and/or linking cubes to find out how many more or how many less. Student will share and discuss different solution strategies of their comparisons and how they know. Sample questions:

• What are you supposed to do in this game? • What story is this puzzle showing/telling? • What are you supposed to find out? • How do you know whether to use the “red grabber” or the “blue filler”? • How do you decide how many to choose? • How is this puzzle different that the other one?

What to look for: How does the student:

• Understand the situation represented in the puzzle? • Explain the situation? • Solve the puzzle? (guess and check, relying on a manipulatives, drawing it out, counting) • Use mathematical language to express the relationship? • Move beyond direct modeling? • Compare the two numbers (just finding the bigger one, or compare the first quantity to the

second?) Extensions: Have students create their own situations of comparing numbers. They can use cubes, or draw. They can share their situations with classmates to figure out. Compare how many more between two two-digit numbers (depending on time of year).

Third Grade Multiplication and Division Fruit Monster Standard: 3.CC.OA.A.3 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Game Description: Determine how many pieces of fruit are needed to feed the monsters. Students explore the relationship between inputs and outputs using ratios within a visual model. Test Drive > 3rd Grade > Multiplication and Division Situations > Fruit Monster

Suggested puzzles:

Level 2

Level 3

Materials: White boards, tiles, linking cubes, and/or game mats Directions: Students solve given puzzles, sharing and discussing different solution strategies focusing on the inverse relationship of multiplication and division. Sample questions: • What are you supposed to do in this game? • How do you decide how many monsters to select? • How are you counting? • Tell me a word problem to show what’s on the screen. • How would you write an expression or equation to show what you are doing? • How would you represent this as repeated addition? As multiplication? • How much fruit is needed for 4 monsters? 6? 10?

What to look for: How does the student: • Figure out how much fruit is needed • Use language to describe a multiplication/division situation • Use counting/multiplication/division to find the solution • Represent the situation with expressions/equations

Extension: • Give the students Fruit Monster Game Mat (make multiple copies of the Fruit Monster mat and let the

students create their own). Have the students create “what if” situations by filling in the key, fruit monsters below, or fruit. Trade with a partner and have each partner try to solve the problem. (For example: “One monster eats 5 fruit?” “What if you had 20 bananas? What if you had 3 monsters?

• Choose a rate such as 3 fruit for 1 monster. Have students create a table to show multiple solutions. Look for patterns.

• Have students create a word problem based on the puzzle.

Fourth Grade Mixed Numbers Mixed Numbers Standard: 4.CC.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Game Description: Plot the combined length of a collection of rectangles on the number line. Test Drive > 4th Grade > Mixed Numbers > Mixed Numbers on the Number Line > Scale Fraction, Levels 2 and 3 Suggested puzzles:

Level 2

Level 3

Materials: Blank paper for writing number lines.

Directions: Teacher/students pose questions about the relationship between the visual model, number line, and the relationship to the unit fraction.

Sample questions: • What fractions do you see in the visual model? Do you see fourths? How many? • How would you represent this model on the number line? • What is the relationship between the whole block vs. the fractional blocks? • How would you plot 5/4 on the number line? 15/4?

What to look for: How does the student: • Explain the fractions they see in the visual model. (Do they understand the 1 = 4/4 which is ¼ + ¼ + ¼ + ¼ ) • Understand how fractions are represented on a number line. (ex. Fractions between 0 and 1, 1 and 2). • Represent the model on the number line. (Can they convert the whole number to unit fractions?) • Explain the relationship between the visual model representation and the number line representation.

Extensions: • Plot a fraction on a number line and students create a visual representation of the fraction. • Give students an “open” number line and give them a mixed number. Have students determine how to

iterate the line to plot the mixed number. Have the students plot the mixed number on the number line.

Fourth Grade Adding and Subtracting Fractions

Scale Fractions

Standard: 4.CC.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 4.CC.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Game Description: Add and subtract fractions and mixed numbers on the number line. The fractions and mixed numbers are presented using visual models. Test Drive -> Adding and Subtracting Fractions -> Scale Fractions -> Level 5 Suggested puzzles:

Level 5

Level 5

Materials: Blank paper for writing number lines. Directions: Show a puzzle from level 1. Discuss what students notice. Discuss how the bars animate to be added together on the Number Line. Discuss if the fractions must be added last. Get some puzzle wrong and discuss what students think will happen and what happens Sample questions: •   What mathematics do you see in this puzzle? •   How does the model (bars and parts) relate to the number line? •   What are some things you need to understand about units to be able to solve this puzzle? •   Where do you see 5/4 in this problem? How about 6/4?

What to look for: How does the student: •   Explain the fractions they see in the visual model. (Can they see wholes and parts in the model? On the

number line?) •   Understand the relationship between mixed numbers and improper fractions. (Do they understand the 1 ¼

= 5/4 which is ¼ + ¼ + ¼ + ¼ + ¼ ) •   Represent addition and subtraction on the number line. •   Explain the relationship between the visual model representation and the number line representation. Extensions: •   Estimate where 8/4 – 3/3 might be on a number line. Explain your thinking.

•   Give students an “open” number line and give them an addition or subtraction problem with mixed numbers. Have students determine how to model the problem on the number line. They will have to determine how to iterate the line to model the problem.  

Fifth Grade Using Parenthesis Multiplying with Parentheses

Standard: 5. CC.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Game Description: Learn the meaning of and how to simplify expressions involving variables and parentheses.

Test Drive -> 5th Grade -> Using Parentheses -> Multiplying with Parentheses-> Level 3 and Level 4

Suggested Puzzles:

Level 3

Level 3

Level 4

Materials: Cubes, Grid Paper Directions: • Give out cubes and/or grid paper. Project a puzzle from level 3. Have the students work to model the

expression represented in the puzzle with their cubes or grid paper. Have students work in groups to discuss their models and how they represent the expression in the puzzle. Select some students to share their models and how their models represent the expression. Discuss how changing the parenthesis or the coefficient would change the visual model.

Sample questions: • What is this expression describing? • How do you express this relationship visually? • How did you solve this puzzle? • How does moving the parentheses affect the solution?

What to look for: How does the student: • Represent the problem visually. (Do they simplify within the parenthesis first? Can they explain why they

simplified it first?) • View the role of the parenthesis. (Can they explain how removing the parenthesis would affect the problem?) • See multiplication in the expression. (Do they know why 4b is 4 x b? Can they identify the groups within the

expression? Ex. 2 (y + y) = 2 groups of y + y) Extensions: • Give students a solution (Ex. 15y) and have them model with the cubes or grid paper equations with

parenthesis that can be used to reach the given solution. Have them write them down. Compare equations from various students and discuss the important structure that parenthesis provide to a problem.

Sixth Grade and Sixth Grade MSS Applying Rates and Ratios Seed Worm

Standard: 6.CC.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Game Description: Select the number of increments, the length of the increment, or the total distance, when given the other two.

Test Drive -> 6th Grade -> Applying Rates and Ratios -> Seed Worm -> Level 2 Test Drive -> 6th Grade MSS -> Applying Rates and Ratios -> Seed Worm -> Level 2 Suggested puzzles:

Level 2

Level 2

Materials: Linking cubes, graph paper (create tape diagrams, bar models) Directions: • Play a puzzle from level 1 and have an informal discussion about the relationship between the worm, the

green growth bars, the vines, and the seed-drop point. • Project a puzzle from level 2. Students use manipulatives or diagrams to show the solution, explaining on

paper how they solved it. When shown the second puzzle, students compare the two situations.

Sample questions: • What do the green bars mean? What are you trying to figure out in this puzzle? • Describe the relationship between the worm and the green growth bars? The green growth bars and the

vine? The vine and the seed drop point? • How do you decide how many spaces to stretch the worm? • How could you write out the relationship you used to solve this mathematically? • What proportions are you using to solve this puzzle? How many different ratios can we write?

What to look for: How does the student: • Explain the question each puzzle is asking? • Represent the solution on paper? • Solve the puzzle (Is the student counting or using ratios)? • Use formal and informal understandings of proportions? • Use language, including symbols to express ratios and proportions? Extension: • Have the students model the relationships between tape diagrams and double number lines. • Have the students model what would happen if the worm in their puzzle was longer, shorter, or an extra

growth bar was added. • Have students create their own puzzles, moving the unknown to different positions. Share or have a partner

solve. Are there puzzles that can’t be solved or have multiple solutions? • Use one-inch grid paper and then draw a given length of a worm. The student can decide the length of the

green growth bars. The student can draw every place a seed would be dropped. They would have to determine how many green growth bars to drop a seed in each location.*

*Allows for good discussion on rate and consistency.

Seventh Grade MSS: Proportional Reasoning Ratio Monster

Standard: 7.CC.RP.2 Recognize and represent proportional relationships between quantities. Game Description: Select a number of monster arms and mouths according the given ratio. In the last level, chose a ratio first and then select the parts. Seventh Grade MSS -> Proportional Reasoning -> Ratio Monster -> Level 3 and Level 4 Suggested puzzles:

Level 3

Level 4

Materials: Unifix Cubes, Paper and Pencil

Directions: • Play a puzzle from level 1 of the Ratio Monster Game to introduce students to the game. Have an informal

discussion about what they notice happening in the puzzle. • Give out materials. Project a puzzle from level 3. Have the students work to solve the puzzle using the cubes

or paper and pencil. Allow opportunities for students to share different strategies. • Project the puzzle from level 4. Compare what is being asked. Compare the strategies used to solve the

puzzles on the two different levels.

Sample questions: • What is the question that we need to solve in this puzzle? • What is the relationship between the monster and its parts, and the parts to each other? • How did you determine those relationships? How do those help you solve the puzzle? • How can you use that information to find the number of parts for n monsters? • In Level 4, how does the way you build the monster affect your solution? How many different solutions are

possible? What to look for: How does the student: • Find the answer for the puzzle (write a proportion, count, group, add, multiply, divide, etc.) • Connect their strategies to ratios and proportions? (Look for evidence in their explanation.) • Express their solutions symbolically?

Extensions: • Have the students build out tables for the puzzles. Review the tables to determine the relationships and write

proportions that can be used to find n monsters. • Show students the pieces to build ____ monsters, have them determine how many parts it takes to build 1.

(Ex. Give students 15 eyes and 10 mouths, if that is what is needed to make 5 monsters, how many eyes and mouths are on one monster?) Share solution strategies.

Eighth Grade MSS: Solving Linear Equations Rolling Equation

Standard: 8.CC. EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms Game Description Students will select a pair of numbers (all positive) that fit the relationship (additive, multiplicative, or both) displayed by visual representation of jumps on the number line, including variables on both sides.

Eighth Grade MSS -> Solving Linear Equations -> Rolling Equation -> Level 2 and Level 3

Suggested puzzles:

Level 2

Level 3

Materials: Paper and pencil

Directions: • Play a puzzle from level 1 of Rolling Equations to introduce students to the game. Have an informal

discussion about what they notice happening in the puzzle. • Project a puzzle from level 2. Have the students work to solve the puzzle using the materials provided. Allow

opportunities for students to use different strategies. Sample questions: • What is the question that we need to solve in this puzzle? • What are the relationships that you see in the puzzle? • How is what you select for the value of x affect the equation? • What is the role of the number line for this puzzle? What is it showing you? • What is the relationship between the two equations on the number line? • How did you get to a solution for this puzzle? • What equations can you write to represent the puzzle?

What to look for: How does the student: • Think about the variable in the problem. (Do they understand the relationship between the variables on top

and the variables on bottom? Do they understand that 4a means each a is equal in value?) • Use the information they see in the puzzle to create their equations (Do they understand the equation on the

bottom is equal to the equation on the top?) Extensions: • Give students number lines (or have them fold their papers in half) and have them create their own

equations for additional puzzles. Students can trade their equations with a classmate to solve.

High School Unit Rates, Tables, and Graphs Monster Graphs Standard: 7.CC.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate Game Description: Given a rate, plot equivalent rates on a graph. High School -> Unit Rates, Tables, and Graphs -> Module 2 -> Monster Graphs -> Level 6

Suggested Puzzles:

Level 6

Level 6

Materials: Grid paper and pencil Directions: • Play a puzzle from level 3 of the Monster Graphs Game to introduce students to the game. Have an informal

discussion about what they notice happening in the puzzle. • Project a puzzle from level 6. Have the students work to solve the puzzle using the grid paper. Allow

students to share how they found their answers. Sample questions: • What is the question(s) that we need to solve in this puzzle? • How does the ratio that is represented on the card/key relate to the graph? How can it help you find your

solution? • Do you notice anything special about the points you plot on the graph? (They are linear) • How does this knowledge help to find the number of pies for n number of fruit monsters?

What to look for: How does the student: • Figure out where to graph the points. (Can students correctly identify the variables represented by the

monsters and the pies as it relates to the x and y axis?) • Determine the placement on the graph when they are dealing with parts instead of whole. (What strategies

do they use to determine the proportional relationship?) Extensions: • Have the students build out a table for a couple of puzzles. • Give students a graph with 3 points plotted. Have them determine the proportional relationship between the

fruit monsters and the pies based on the given plotted points. • Have students create their own graphs when given a ratio.