Critical Questions for Investigations First Grade

Critical Questions for Investigations First Grade

Mathematical Thinking

Mathematical Thinking

Investigation 1: Exploring Materials
1 Getting Started with Materials What do you notice about …? (CU)
2,3,4 Exploring Materials How do you know there are 20? (RL)

Investigation 2: Exploring Numbers
1 The Game of Compare Which is larger? Why? (RL)
2,3 Introducing the Staircases and Choice Time What number comes next? What number came before? (SP, RL)
4 Seven Peas and Carrots How many more peas or carrots will you need to make seven? (SP)
5,6 Number Choices Tell me how you recorded your solution. (CU)

Investigation 3: Patterns
1 What Comes Next? What comes next? How do you know? (SP, RL)
2 Clapping Patterns How did you record your pattern? (CU)
3,4 Finding and Making Patterns What makes these patterns the same or different? (CU, MC)
5,6 What is a Pattern? Is this a pattern? How do you know? (CU, RL)

Investigation 4: Counting and Combining
1 Collect 15 Together How many more do you need to make 15? (SP, RL)
2,3 Counting and Combining Can you predict what comes next? (RL)
4 Eleven Fruits
Assessment
How many of each could you have? (SP)
5 Making Predictions About a Story What happens next? (RL)
6 How Many In All? How many animals were in each group? How many in all? (SP)

Investigation 5: Data About Our Class
1 Kid Pins How many pins do we need for…? (SP)
2 Attendance and Other Surveys Which has more? How much more? (SP, RL)
3,4 Inventing Survey Representations What are the categories? How many people in each? (SP, MC)
5,6 How We Got To School Today

What does your representation show? (CU, MC)

Building Number Sense

Building Number Sense

Investigation 1: Visualizing Numbers
1 Quick Images How many dots did you see and how do you know? (RL)
2 Compare Dots Which card has more dots? Which card has less dots? (SP)
3,4 Copying Cubes How did you count the objects? (CU)
5,6 Number Shapes How can you check to make sure you have counted correctly? (RL)
7,8 Making Dot Pictures How did you find the total number of pattern blocks? (CU, SP)
9 How Many Dots? How would you arrange 6 dots on a paper so it is easy to count? (CU)

Investigation 2: Building Numbers in Different Ways
1 Twelve Cats and Dogs How many of each do you have to equal 12? (SP)
2 Problems About Ten How did you solve the problem? (CU)
3 The Game of Double Compare Which is larger? How do you know? (RL)
4,5 Breaking Numbers Into Two Parts Which is larger? How do you know? (RL)
6,7,8 Towers of 10 and Number Choices How many more do you need to make 10? (SP, RL)
9 Three Towers
Assessment
How are you keeping track of the numbers of cubes in your towers? (CU)

Investigation 3: Counting
1,2 The 100 Chart How do you know what numbers are missing? (SP, RL)
3,4 Which Holds More? Which container holds more? How do you know? (SP, RL, MC)
5,6,7 More Counting and Comparing How do you know you have counted every counter? (RL)
8 Clapping Patterns What color cube will be next in the pattern? (RL)

Investigation 4: Addition and Subtraction
1 Introducing Combining Situations Is your answer going to be more or less than the separate amounts you started with? How do you know? (SP, RL)
2 Introducing Separating Situations Is your answer going to be less or more than the number you started with? How do you know? (SP, RL)
3,4,5 Five-In-A-Row and Story Problems What is the sum of 6 and 3? How do you know? (SP, RL)
6 Dot Addition How did you figure out this combination? Is there another way? (SP,CU)
7,8,9 Combining and Separating What number can we make with three 2’s? What other numbers could we make with just 2’s? (SP, RL, MC)
10 Solving Story Problems
Assessment
What is happening in this problem? Is it combining or separating? (SP,RL, MC)

Bigger, Taller, Heavier, Smaller

Investigation 1: Weighing and Balancing
1,2 Exploring Weight How can you tell which object is lighter or heavier? (RL, MC)
3,4 Comparing Two Objects

Can you predict which will be heavier or lighter? (RL, MC)
5,6 Balancing Groups of Objects How do you know when it is equal? (RL, MC)

Investigation 2: Filling
1 A Cupful of Sand How will you know when your cup is full? (RL, MC)
2,3,4 Filling Space

Which container will hold more? Why? (SP,RL)
5,6,7 Comparing Containers How are you keeping track? (CU, SP,MC)

Investigation 3: Measuring Length
1 Longer Than, Shorter Than How did you figure out which was the longest side? (CU, SP)
2 Measuring with Hands and Feet Which measurement do you think was most accurate? Why? (CU)
3 Feet Lengths What is your strategy for putting the objects in order? (CU, SP)
4,5 Measuring with Cubes What do you do when a length is not close to a number of whole cubes? (SP, CU)

Quilt Squares and Block Towns

Quilt Squares and Block Towns

Investigation 1: Shapes and Patterns
1 What Shapes Do You See? What shapes do you see? (CU)
2 Same Shape, Different Shape How did you keep track of the different pattern blocks when you were counting? (CU)
3,4,5,6 Describing 2-D Shapes How if you had a yellow hexagon, what other blocks could you trade for? (SP, CU)
7 Three Ways to Fill an Outline
Assessment
How many blocks did you use? How did you figure that out? (SP)
8,9,10 Filling Shapes
Assessment
Is that the most possible blocks you can use? How do you know? (RL)
11,12 Sorting 2-D Shapes
Assessment
Why did you put these shapes together? (RL, CU)
13,14,15 Quilts with Squares and Triangles Describe your pattern. (CU)

Investigation 2: Comparing and Constructing 3-D Shapes
1,2 Describing and Comparing Shapes How do you know you have the correct number of cubes? (RL)
3 Block Patterns
Assessment
Was it easy or hard to find a block that…? (CU)
4,5,6 Blocks in a Sock How could you tell by feel which picture the block matched? (CU)
7 What Kind of Box Is It? What is a face of a box? (CU)
8,9,10 Making Boxes
Assessment
Which pieces did you choose to make your box? Why? (RL, CU)

Investigation 3: Building a Block Town
1,2 Drawing Geo-blocks
Assessment
Which part of the building does your drawing show? (CU)
3,4 Planning Town What kinds of buildings do we need? (CU, MC, SP)
5 Building a Town
Assessment
Does your plan match your building? How do you know? (SP, RL,MC)
6,7 Giving Directions What are the directions to get from your building to ____? (CU, MC)

Number Games and Story Problems

Number Games and Story Problems

Investigation 1: Number Combinations
1 Pictures of 10 How did you remember what the picture looked like? (RL, CU)
2,3 Number Combinations What is another way to show…? (SP,CU)
4,5 Total of 10 What is one way you made ___ with your cards? (CU, RL)
6 How Many of Each Color?
Assessment
What is another combination of 10 you could make with 3 colors? (SP)
7,8,9 Crayon Puzzles
Assessment
How did you solve the puzzle? (CU)

Investigation 2: Twos, Fives and Tens
1 How Many Hands?
Assessment
How did you figure out how many hands? (CU, RL)
2 Twos and Fours How did you figure out how many …? (RL)
3 Collect 25¢ Together If I rolled a 7 what coins would I take? (SP)
4,5 Counting and Combining How did you find the total number of squares? (SP)
6,7,8 Numbers to 100 What patterns do you see? (CU)
9 Patterns of Fives and Tens What can you tell me about this pattern? Who has another idea? (CU)
10,11,12 Twos, Fives, and Tens
Assessment
How many more do we need?
What is another way to figure that out?
How many extra?
(SP, RL, CU)

Investigation 3: Addition and Subtraction
1 Combining Situations
Assessment
What is your strategy for combining? (SP, CU)
2 Separating Situations
Assessment
What is your strategy for separating? (SP, CU)
3,4,5 Five-In-a-Row and Story Problems How did you find that out? (RL, CU)
6,7,8 Tens Go Fish
Assessment
If I draw a 6 what card should I ask for to get 10? (SP)
9 Combining with Unknown Change Does your story match the equation? (CU,MC)
10,11,12 Addition and Subtraction What number did you start on to count by when you were combining or separating? Why? (RL,MC)
13 Solving Story Problems
Assessment
What was hard or easy for you in this unit? Why? (CU, MC)

First Grade Critical Questions

1 Getting Started with Materials	What do you notice about …? (CU)
2,3,4 Exploring Materials	How do you know there are 20? (RL)

1 The Game of Compare	Which is larger? Why? (RL)
2,3 Introducing the Staircases and Choice Time	What number comes next? What number came before? (SP, RL)
4 Seven Peas and Carrots	How many more peas or carrots will you need to make seven? (SP)
5,6 Number Choices	Tell me how you recorded your solution. (CU)

1 What Comes Next?	What comes next? How do you know? (SP, RL)
2 Clapping Patterns	How did you record your pattern? (CU)
3,4 Finding and Making Patterns	What makes these patterns the same or different? (CU, MC)
5,6 What is a Pattern?	Is this a pattern? How do you know? (CU, RL)

1 Collect 15 Together	How many more do you need to make 15? (SP, RL)
2,3 Counting and Combining	Can you predict what comes next? (RL)
4 Eleven Fruits Assessment	How many of each could you have? (SP)
5 Making Predictions About a Story	What happens next? (RL)
6 How Many In All?	How many animals were in each group? How many in all? (SP)

1 Kid Pins	How many pins do we need for…? (SP)
2 Attendance and Other Surveys	Which has more? How much more? (SP, RL)
3,4 Inventing Survey Representations	What are the categories? How many people in each? (SP, MC)
5,6 How We Got To School Today	What does your representation show? (CU, MC)

1 Quick Images	How many dots did you see and how do you know? (RL)
2 Compare Dots	Which card has more dots? Which card has less dots? (SP)
3,4 Copying Cubes	How did you count the objects? (CU)
5,6 Number Shapes	How can you check to make sure you have counted correctly? (RL)
7,8 Making Dot Pictures	How did you find the total number of pattern blocks? (CU, SP)
9 How Many Dots?	How would you arrange 6 dots on a paper so it is easy to count? (CU)

1 Twelve Cats and Dogs	How many of each do you have to equal 12? (SP)
2 Problems About Ten	How did you solve the problem? (CU)
3 The Game of Double Compare	Which is larger? How do you know? (RL)
4,5 Breaking Numbers Into Two Parts	Which is larger? How do you know? (RL)
6,7,8 Towers of 10 and Number Choices	How many more do you need to make 10? (SP, RL)
9 Three Towers Assessment	How are you keeping track of the numbers of cubes in your towers? (CU)

1,2 The 100 Chart	How do you know what numbers are missing? (SP, RL)
3,4 Which Holds More?	Which container holds more? How do you know? (SP, RL, MC)
5,6,7 More Counting and Comparing	How do you know you have counted every counter? (RL)
8 Clapping Patterns	What color cube will be next in the pattern? (RL)

1 Introducing Combining Situations	Is your answer going to be more or less than the separate amounts you started with? How do you know? (SP, RL)
2 Introducing Separating Situations	Is your answer going to be less or more than the number you started with? How do you know? (SP, RL)
3,4,5 Five-In-A-Row and Story Problems	What is the sum of 6 and 3? How do you know? (SP, RL)
6 Dot Addition	How did you figure out this combination? Is there another way? (SP,CU)
7,8,9 Combining and Separating	What number can we make with three 2’s? What other numbers could we make with just 2’s? (SP, RL, MC)
10 Solving Story Problems Assessment	What is happening in this problem? Is it combining or separating? (SP,RL, MC)

1,2 Exploring Weight	How can you tell which object is lighter or heavier? (RL, MC)
3,4 Comparing Two Objects	Can you predict which will be heavier or lighter? (RL, MC)
5,6 Balancing Groups of Objects	How do you know when it is equal? (RL, MC)

1 A Cupful of Sand	How will you know when your cup is full? (RL, MC)
2,3,4 Filling Space	Which container will hold more? Why? (SP,RL)
5,6,7 Comparing Containers	How are you keeping track? (CU, SP,MC)

1 Longer Than, Shorter Than	How did you figure out which was the longest side? (CU, SP)
2 Measuring with Hands and Feet	Which measurement do you think was most accurate? Why? (CU)
3 Feet Lengths	What is your strategy for putting the objects in order? (CU, SP)
4,5 Measuring with Cubes	What do you do when a length is not close to a number of whole cubes? (SP, CU)

1 What Shapes Do You See?	What shapes do you see? (CU)
2 Same Shape, Different Shape	How did you keep track of the different pattern blocks when you were counting? (CU)
3,4,5,6 Describing 2-D Shapes	How if you had a yellow hexagon, what other blocks could you trade for? (SP, CU)
7 Three Ways to Fill an Outline Assessment	How many blocks did you use? How did you figure that out? (SP)
8,9,10 Filling Shapes Assessment	Is that the most possible blocks you can use? How do you know? (RL)
11,12 Sorting 2-D Shapes Assessment	Why did you put these shapes together? (RL, CU)
13,14,15 Quilts with Squares and Triangles	Describe your pattern. (CU)

1,2 Describing and Comparing Shapes	How do you know you have the correct number of cubes? (RL)
3 Block Patterns Assessment	Was it easy or hard to find a block that…? (CU)
4,5,6 Blocks in a Sock	How could you tell by feel which picture the block matched? (CU)
7 What Kind of Box Is It?	What is a face of a box? (CU)
8,9,10 Making Boxes Assessment	Which pieces did you choose to make your box? Why? (RL, CU)

1,2 Drawing Geo-blocks Assessment	Which part of the building does your drawing show? (CU)
3,4 Planning Town	What kinds of buildings do we need? (CU, MC, SP)
5 Building a Town Assessment	Does your plan match your building? How do you know? (SP, RL,MC)
6,7 Giving Directions	What are the directions to get from your building to ____? (CU, MC)

1 Pictures of 10	How did you remember what the picture looked like? (RL, CU)
2,3 Number Combinations	What is another way to show…? (SP,CU)
4,5 Total of 10	What is one way you made ___ with your cards? (CU, RL)
6 How Many of Each Color? Assessment	What is another combination of 10 you could make with 3 colors? (SP)
7,8,9 Crayon Puzzles Assessment	How did you solve the puzzle? (CU)

1 How Many Hands? Assessment	How did you figure out how many hands? (CU, RL)
2 Twos and Fours	How did you figure out how many …? (RL)
3 Collect 25¢ Together	If I rolled a 7 what coins would I take? (SP)
4,5 Counting and Combining	How did you find the total number of squares? (SP)
6,7,8 Numbers to 100	What patterns do you see? (CU)
9 Patterns of Fives and Tens	What can you tell me about this pattern? Who has another idea? (CU)
10,11,12 Twos, Fives, and Tens Assessment	How many more do we need? What is another way to figure that out? How many extra? (SP, RL, CU)

1 Combining Situations Assessment	What is your strategy for combining? (SP, CU)
2 Separating Situations Assessment	What is your strategy for separating? (SP, CU)
3,4,5 Five-In-a-Row and Story Problems	How did you find that out? (RL, CU)
6,7,8 Tens Go Fish Assessment	If I draw a 6 what card should I ask for to get 10? (SP)
9 Combining with Unknown Change	Does your story match the equation? (CU,MC)
10,11,12 Addition and Subtraction	What number did you start on to count by when you were combining or separating? Why? (RL,MC)
13 Solving Story Problems Assessment	What was hard or easy for you in this unit? Why? (CU, MC)