Greater Than, Less Than, Equal Kindergarten More Less ...

Kindergarten

Greater Than, Less Than, Equal To

More Less Parachute

Standard: .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: .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: .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: .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.

.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: .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: .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 ? + ? + ? + ? ) ? 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

Scale Fractions

Fractions

Standard: .NF.B.3a

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

.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 ?

= 5/4 which is ? + ? + ? + ? + ? ) ? 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.

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