Critical Questions for Investigations Kindergarten
Mathematical Thinking

Pattern Trains and Hopscotch Paths
Collecting, Counting and Measuring
Counting Ourselves and Others
Making Shapes and Building Blocks

Investigation 1: Counting and Measuring
Investigation 2: Six Tiles
Investigation 3: Story Problems
Investigation 4: Blue and Red Crayons

Critical Questions for Investigations Kindergarten

Critical Questions for Investigations Kindergarten

Mathematical Thinking

Mathematical Thinking

Investigation 1: Attendance
FT Attendance

How should we figure out the total number of children? (SP)
CT Exploring Color Tiles Describe your tiles and creation. (CU)
Can you make a pattern? (SP)
CT Exploring Pattern Blocks

Assessment
Describe your pattern blocks. (CU)
Can you make one pattern block by using other combinations? (SP)
Describe your geo-blocks.
Can you make one geo-block by using other combinations? (SP)

Investigation 2: Counting Jar
FT Counting Jar How can we show that there are ___ ___ in the jar? (RL)
CT Counting Jar How do you know that you have the same number as in the jar? (RL)

Investigation 3: Calendar
FT Calendar

What do you notice about the calendar? (PS,MC)
Where is today on the calendar? (MC)
CT Exploring Interlocking Cubes What did you create with your cubes? (CU)
Can you build something with only 15 cubes? (SP)

Investigation 4: Today’s Question
FT Today’s Question What does this chart tell us about our class? (RL)
Are the two groups equal?
What is the difference? (CU, MC)

Pattern Trains and Hopscotch Paths

Pattern Trains and Hopscotch Paths

Investigation 1: Exploring Patterns
FT: Watching and Looking What comes next in the pattern? (SP)
FT: Cubes: What Do You Notice What is different about these two patterns? (CU, MC)
CT: Making Patterns

Assessment
What is your pattern? (CU)
CT: What’s Missing? How did you figure out what was missing? (RL)

Investigation 2: What Comes Next?
FT: Patterns on the Pocket Chart What comes next? (SP) How do you know? (RL)
CT: What Comes Next? What part of your pattern repeats? (RL)
CT: Pattern Block Snakes Can you read your pattern to me? (CU)
CT: Add On How many times does your pattern repeat? (RL)
CT: Break the Train What kind of patterns do you see in the room/art/building, etc.? (MC)
CT: Make a Train What color do you need to roll next? (RL)

Investigation 3: Hopscotch Paths
FT: Hopscotch and Tile Paths Can you describe your path? (CU)
CT: Hopscotch Paths How many times does your pattern repeat? (RL)
CT: Tiles Paths Can you identify your repeating pattern? (CU)

Investigation 4: Pattern Borders
CT: FT: Pattern Borders
Assessment
What happens when we reach the top of the chart? (RL)
CT: Color Tile Borders Can you predict what color this square will be? (RL)
CT: Twelve Chips Can you make a different pattern with your chips? (SP)

Collecting, Counting and Measuring

Investigation 1: Counting Books
FT: Counting Books How did you know how many objects to draw on each page? (RL)
CT: My Counting Book
Count Us In – game 2
How do you know how many cubes to color on your strip? (RL)
CT: Grab and Count Is this more than ___ or less than ___?
How do you know? (RL)
CT: Counting Jar How did you count the things in the jar? (SP)

Investigation 2: Taking Inventory
FT: Taking Inventory
Assessment
How did you organize the objects so you could count them? (SP)
CT: Inventory Bags
Count Us In – game 3
What would you do if you got two different counts for the same group of objects? (SP)

Investigation 3: Comparing Towers
FT: Measurement Towers How could you compare to show which is shorter? (SP)
CT: Measuring Table How did you sort the objects into the two different categories? (MC, CU)
CT: Grab and Count – Which Has More? Which has more?
How do you know?
(RL)
CT: Compare How did you know which number was larger? (RL)

Investigation 4: Counting and Comparing
FT: Letters In Our Names
Assessment
How did you figure out how many letters were in your name? (RL)
CT: Comparing Names How do you know where to place a name? (RL, MC)
CT: Grab and Count – Compare Which tower has the most? Which has the least? (SP)
CT: Collect 10 Together How do you know you have 10 counters? (RL)

Investigation 5: Least to Most
FT: Least to Most How did you compare your handfuls to put them in order? (SP)
CT: Grab and Count – Least to Most
Assessment
Can you show me which tower has the most/least? (CU)
CT: Racing Bears How many moves do I have left? How do you know? (RL)

Investigation 6: Arrangements of Six
FT: Six Tiles How can we arrange these tiles to show six? (SP)
CT: Books of Six
Assessment
Could you think of another way to make six? (SP)

Counting Ourselves and Others

Counting Ourselves and Others

Investigation 1: How Many Are We?
FT: How Many Are We? How do you know your model/picture shows exactly the number of students in the class? (RL, CU)
FT: Counting Noses, Counting Eyes What can you tell me about the eye chart? (SP)
CT: Self Portraits How would you sort the pictures? (CU,SP,MC)
CT: Counting Chairs How did you count the number of chairs? (SP, CU)
CT: Pattern Block Grab What did you record to represent the blocks? (CU)

Investigation 2: What Did You Eat For Lunch?
FT: What Did You Eat For Lunch? Which group does ___ (food) belong in? Why? (RL, MC)
CT: Same and Different What things in this room are the same? Different? (SP, MC)
CT: Boxes, Bottles, and Cans Why did you organize the objects in these groups? (RL, MC)
CT: The Grocery Store Why does the way you organized the store work? (RL,MC)
CT: The Clothing Sort Can you sort the clothes another way? (SP)

Investigation 3: Collecting Data About Our Class
FT: Yes/No Surveys

What do you notice about this survey? (CU,MC)
CT: Yes/No Surveys

Assessment
How do you know if you have surveyed everyone in the class? (RL)

Investigation 4: Collecting Data About Our Class
FT: Who’s Here? Who’s Not?
Assessment
How did you figure out how many are here today? (SP, CU)

Making Shapes and Building Blocks

Making Shapes and Building Blocks

Investigation 1: Shapes Around Us
FT: Looking at 2-D Shapes What could you make with a square? (MC, SP)
CT: Book of Shapes What did you notice about the shapes? (CU,MC)
CT: Pattern Block Pictures How did you copy your design? (RL)
CT: Shape Mural What shapes did you use the most? Why? (RL)

Investigation 2: Exploring Shapes with the Computer
FT: Introducing the Shapes Software What did you like about using the computer today? (CU)
CT: Free Explore with Shapes How did you move shapes on the screen? (CU)
CT: Pattern Block Puzzles Is there another way to make a yellow hexagon?
(SP)

Investigation 3: Looking at 3-D Shapes
FT: 3-D Shapes in the Classroom What did you find that looked like a sphere?
(CU, MC)
CT: Shape Hunt
Assessment
What did you find that looked like a rectangular hexagon? (CU, MC)
CT: Exploring Geo-Blocks How are the geo-blocks different from the pattern blocks? (RL)
CT: The Shape of Things on the Computer Which puzzle did you like the best? Why? (CU)

Investigation 4: Making Shapes and Building Blocks
FT: Clay Shapes What kinds of shapes did you make with the clay? (CU, MC)
CT: Clay Shapes Tell me about your shape.(CU)
CT: Fill the Hexagons Can you fill a yellow hexagon in two different ways? (SP)
CT: Build a Block How did you build the larger block? (RL, CU)
CT: Quick Images on the Computer How did you remember what the picture looked like? (RL)

Investigation 5: 2-D Faces on 3-D Blocks
FT: A Close Look at Geo-Blocks How are the faces the same? Different? (RL)
CT: Matching Faces Show me how many blocks you found that had matching faces? (CU)
CT: Geo-Block Match-Up Were there different blocks that matched the same outline? Why or why not? (RL)
CT: Planning Pictures on the Computer Was it easy or hard to copy your design on the computer? Why? (CU)

How Many In All?

How Many In All?

Investigation 1: Counting and Measuring
FT: Counting and Measuring How many sticks do you think we will need to measure ___? (SP)
CT: Measuring with Sticks Why did we get different measurements for the same length? (RL)
CT: Measuring with Cubes
Assessment
Does it make a difference to snap the cubes together or leave them loose? (RL)
CT: Collect 15 Together Is that more or less than 15? How do you know? (RL)
CT: Inventory Bags How are you going to show your counting on paper? (CU, MC)

Investigation 2: Six Tiles
FT: Six Tiles in All Does your shape fit the rule? Why or why not? (RL)
CT: Books of Six in All Did you use 6 tiles in every picture? Why or why not? (RL)
CT: Grab Two Handfuls How many do you think you can grab? Who has more? (RL)
CT: Tower of Six How many more do we need to get to 6? (SP)

Investigation 3: Story Problems
FT: Story Problems Was the story about putting groups together or about taking away part of a group? (RL, MC)
CT: Double Compare Who has more? How do you know? (RL)
CT: Counter in a Cup How many counters did I hide? How do you know? (RL)
CT: Racing Bears How many moves do I have left? (SP)

Investigation 4: Blue and Red Crayons
FT: Five Crayons in All
Assessment
How many do I need of each to make 5? (SP)
CT: Six Crayons in All How many do I need of each to make 6? (SP)
CT: Total of Six
Assessment
What card could I put together with this ___ to make six? (SP)

Kindergarten Critical Questions

FT Attendance	How should we figure out the total number of children? (SP)
CT Exploring Color Tiles	Describe your tiles and creation. (CU) Can you make a pattern? (SP)
CT Exploring Pattern Blocks Assessment	Describe your pattern blocks. (CU) Can you make one pattern block by using other combinations? (SP)
	Describe your geo-blocks. Can you make one geo-block by using other combinations? (SP)

FT Counting Jar	How can we show that there are ___ ___ in the jar? (RL)
CT Counting Jar	How do you know that you have the same number as in the jar? (RL)

FT Calendar	What do you notice about the calendar? (PS,MC) Where is today on the calendar? (MC)
CT Exploring Interlocking Cubes	What did you create with your cubes? (CU) Can you build something with only 15 cubes? (SP)

FT: Watching and Looking	What comes next in the pattern? (SP)
FT: Cubes: What Do You Notice	What is different about these two patterns? (CU, MC)
CT: Making Patterns Assessment	What is your pattern? (CU)
CT: What’s Missing?	How did you figure out what was missing? (RL)

FT: Patterns on the Pocket Chart	What comes next? (SP) How do you know? (RL)
CT: What Comes Next?	What part of your pattern repeats? (RL)
CT: Pattern Block Snakes	Can you read your pattern to me? (CU)
CT: Add On	How many times does your pattern repeat? (RL)
CT: Break the Train	What kind of patterns do you see in the room/art/building, etc.? (MC)
CT: Make a Train	What color do you need to roll next? (RL)

FT: Hopscotch and Tile Paths	Can you describe your path? (CU)
CT: Hopscotch Paths	How many times does your pattern repeat? (RL)
CT: Tiles Paths	Can you identify your repeating pattern? (CU)

CT: FT: Pattern Borders Assessment	What happens when we reach the top of the chart? (RL)
CT: Color Tile Borders	Can you predict what color this square will be? (RL)
CT: Twelve Chips	Can you make a different pattern with your chips? (SP)

FT: Counting Books	How did you know how many objects to draw on each page? (RL)
CT: My Counting Book Count Us In – game 2	How do you know how many cubes to color on your strip? (RL)
CT: Grab and Count	Is this more than ___ or less than ___? How do you know? (RL)
CT: Counting Jar	How did you count the things in the jar? (SP)

FT: Taking Inventory Assessment	How did you organize the objects so you could count them? (SP)
CT: Inventory Bags Count Us In – game 3	What would you do if you got two different counts for the same group of objects? (SP)

FT: Measurement Towers	How could you compare to show which is shorter? (SP)
CT: Measuring Table	How did you sort the objects into the two different categories? (MC, CU)
CT: Grab and Count – Which Has More?	Which has more? How do you know? (RL)
CT: Compare	How did you know which number was larger? (RL)

FT: Letters In Our Names Assessment	How did you figure out how many letters were in your name? (RL)
CT: Comparing Names	How do you know where to place a name? (RL, MC)
CT: Grab and Count – Compare	Which tower has the most? Which has the least? (SP)
CT: Collect 10 Together	How do you know you have 10 counters? (RL)

FT: Least to Most	How did you compare your handfuls to put them in order? (SP)
CT: Grab and Count – Least to Most Assessment	Can you show me which tower has the most/least? (CU)
CT: Racing Bears	How many moves do I have left? How do you know? (RL)

FT: Six Tiles	How can we arrange these tiles to show six? (SP)
CT: Books of Six Assessment	Could you think of another way to make six? (SP)

FT: How Many Are We?	How do you know your model/picture shows exactly the number of students in the class? (RL, CU)
FT: Counting Noses, Counting Eyes	What can you tell me about the eye chart? (SP)
CT: Self Portraits	How would you sort the pictures? (CU,SP,MC)
CT: Counting Chairs	How did you count the number of chairs? (SP, CU)
CT: Pattern Block Grab	What did you record to represent the blocks? (CU)

FT: What Did You Eat For Lunch?	Which group does ___ (food) belong in? Why? (RL, MC)
CT: Same and Different	What things in this room are the same? Different? (SP, MC)
CT: Boxes, Bottles, and Cans	Why did you organize the objects in these groups? (RL, MC)
CT: The Grocery Store	Why does the way you organized the store work? (RL,MC)
CT: The Clothing Sort	Can you sort the clothes another way? (SP)

FT: Looking at 2-D Shapes	What could you make with a square? (MC, SP)
CT: Book of Shapes	What did you notice about the shapes? (CU,MC)
CT: Pattern Block Pictures	How did you copy your design? (RL)
CT: Shape Mural	What shapes did you use the most? Why? (RL)

FT: Introducing the Shapes Software	What did you like about using the computer today? (CU)
CT: Free Explore with Shapes	How did you move shapes on the screen? (CU)
CT: Pattern Block Puzzles	Is there another way to make a yellow hexagon? (SP)

FT: 3-D Shapes in the Classroom	What did you find that looked like a sphere? (CU, MC)
CT: Shape Hunt Assessment	What did you find that looked like a rectangular hexagon? (CU, MC)
CT: Exploring Geo-Blocks	How are the geo-blocks different from the pattern blocks? (RL)
CT: The Shape of Things on the Computer	Which puzzle did you like the best? Why? (CU)

FT: Clay Shapes	What kinds of shapes did you make with the clay? (CU, MC)
CT: Clay Shapes	Tell me about your shape.(CU)
CT: Fill the Hexagons	Can you fill a yellow hexagon in two different ways? (SP)
CT: Build a Block	How did you build the larger block? (RL, CU)
CT: Quick Images on the Computer	How did you remember what the picture looked like? (RL)

FT: A Close Look at Geo-Blocks	How are the faces the same? Different? (RL)
CT: Matching Faces	Show me how many blocks you found that had matching faces? (CU)
CT: Geo-Block Match-Up	Were there different blocks that matched the same outline? Why or why not? (RL)
CT: Planning Pictures on the Computer	Was it easy or hard to copy your design on the computer? Why? (CU)

FT: Counting and Measuring	How many sticks do you think we will need to measure ___? (SP)
CT: Measuring with Sticks	Why did we get different measurements for the same length? (RL)
CT: Measuring with Cubes Assessment	Does it make a difference to snap the cubes together or leave them loose? (RL)
CT: Collect 15 Together	Is that more or less than 15? How do you know? (RL)
CT: Inventory Bags	How are you going to show your counting on paper? (CU, MC)

FT: Six Tiles in All	Does your shape fit the rule? Why or why not? (RL)
CT: Books of Six in All	Did you use 6 tiles in every picture? Why or why not? (RL)
CT: Grab Two Handfuls	How many do you think you can grab? Who has more? (RL)
CT: Tower of Six	How many more do we need to get to 6? (SP)

FT: Story Problems	Was the story about putting groups together or about taking away part of a group? (RL, MC)
CT: Double Compare	Who has more? How do you know? (RL)
CT: Counter in a Cup	How many counters did I hide? How do you know? (RL)
CT: Racing Bears	How many moves do I have left? (SP)

FT: Five Crayons in All Assessment	How many do I need of each to make 5? (SP)
CT: Six Crayons in All	How many do I need of each to make 6? (SP)
CT: Total of Six Assessment	What card could I put together with this ___ to make six? (SP)