Critical Questions for Investigations Grade 2
Mathematical Thinking
Investigation 1: Exploring Materials
| 1 Exploring Cubes and Arrangements of 10 | How would you describe your arrangement? (CU) |
| 2 Exploring Cubes, Patterns, Blocks and Geo-blocks | Is there anything you notice about the pattern blocks? About the Geo-blocks? (CU) |
| 4 Building and Sorting Cube Things | Why did you choose to sort your blocks the way you did? (SP, RL) |
Investigation 2: Looking at Numbers
| 1 How Many Days Have We Been in School? | How do you use numbers? (CU, MC) |
| 2,3 Card Games | Can you predict which card you will need to draw to get 10? (RL) |
| 6 Today’s Number and Counting Pockets | What did we want to find out? (CU, MC) |
| 8 Ways to Get to 12
Assessment | What is your story for a way to get 12? (CU, MC) |
Investigation 4: Geometric Counts
| 1 Geo-Blocks and Pattern Block Puzzles | How many different ways are there to fill a shape? How do you know when you have found them all? (SP, RL) |
| 3 Counting Geo-Blocks and Pattern Blocks | How many different geo-blocks are in a set? How can you prove that? (SP, RL) |
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5 Sorting Geo-Blocks Assessment | How are your blocks alike or different? (CU) |
Investigation 4: Counting
| 1 Enough for the Class? | If everyone takes one cube, how many cubes will be left in the bag? (SP, RL) How did you solve the problem? (CU) |
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2 Counting Coins, Counting Choices Assessment | What coins might he/she trade his pennies for? (MC, RL) |
| 3,4 Counting Strips and Counting Choices | How did you record your counting? Did you see any patterns to help you? (CU) |
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5 Enough for the Class? Revisited
Assessment | How did you represent the problem? (CU, MC) |
Coins, Coupons and Combinations
Investigation 1: 10’s and Doubles
| 1 Combinations of 20 | How do you know you found all the combinations? (RL) |
| 2,3 Card Games | What would I need to add to ___ to get to 10? (SP) |
| 4,5 Doubles | What happens when you double ___? What does the number sentence look like? (SP) |
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6 Number Strings Assessment | How would you add ___+___+___? (SP) |
| 7 Exploring Calculators | Does the answer make sense? How do you know?(RL) |
| 8,9 Close to 20 and Beat the Calculator – Play game until most students are at recall level. Can use the 10+10 strategy |
How did you solve the number string? (CU) |
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10 Today’s Number and The Magic Pot Assessment | What is another way to make ___? (SP, RL) |
| 11 Counting Pockets | How can we check our answer? (RL) |
Investigation 2: Grouping by 2’s, 5’s, and 10’s
| 1 Using Groups | What patterns do you see? (SP) |
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2 Exploring Multiples of 5
Assessment | What do you notice about the sequence of numbers? (SP) |
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3 Counting By Different Groups Assessment | How did you count up the groups? (CU) |
| 4,5 Counting Choices
Assessment | How do you keep track of what you have counted? (RL) |
| 6 Ways to Make 15¢ | How do you know we have all the combinations? (RL) |
| 7,8,9 Coins and Coupons | What coupons did you find that totaled 50¢? How do you know? (SP, RL) |
| 10 Collecting Pocket Data |
How does the 100 chart help us count? (CU, MC) |
Investigation 3: Introducing Addition and Subtraction Situations
| 1 Introducing Combining Situations | Will the answer be more or less than ___? (SP) |
| 2 Addition Notation | What is a story for ___+___= ? (SP) |
| 3 Introducing Separating Situations | What strategy did you use for the separating situations? (CU) |
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4,5 Making Sense of Addition and Subtraction Assessment | What strategy did you use to check your answer? (RL) |
Investigation 4: One Hundred
| 1 Exploring the 100 Chart | What patterns do you see on the 100 chart? (SP) |
| 2,3,4 Working with 100 | How many more do I need to get to 10 (50, 100)? (SP) |
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5 Penny-a-Pocket Assessment | How did you know which strategy to use? (RL) |
Does It Walk, Crawl, or Swim?
Investigation 1: Sorting People and Yekttis
| 1,2 Collecting and Representing Data About Ourselves |
What does your representation tell us? (CU) |
| 3 Working with Two Attributes | Was it easy or hard to sort with 2 rules? Why? (CU) |
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4,5 Looking at Yekttis Assessment | What are the attributes that the Yekttis have in common? (CU, RL) |
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6 Introducing Venn Diagrams Assessment | How did you know where to place your Yektti? (RL) |
Investigation 2: Collections: What Goes Together?
| 1,2 Exploring Thing Collections | What does your collection not have? (SP, RL) |
| 3,4 Sink and Float
Assessment | Why do you think some things sink and others float? (RL,MC) |
Investigation 3: Animals in the Neighborhood
| 1 How Animals Move | How did you categorize your information? (CU) |
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2,3 Representing Data In More Than One Way Assessment | What does your representation tell us? (CU) |
Shapes, Halves and Symmetry
Investigation 1: Investigation 1: Composing and Decomposing Shapes
| 1 Shapes Around Us | Where do we find rectangles in our classroom? (SP) |
| 2,3 Seeing Shapes within Shapes | How many green triangles does it take to cover a yellow hexagon? (SP) |
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4,5 Shape Puzzles
Assessment | How can you fill a yellow hexagon using three different shapes of pattern blocks? (SP) |
| 6,7,8 Building Buildings | Complete the number pattern: 2,4, __, 6, 8, ___ (SP) |
Investigation 2: What Is a Rectangle?
| 1 Investigating Quadrilaterals | What shapes have only four sides? (SP) |
| 2 Which Rectangle Is the Biggest? | Which is the biggest – shape A or shape C? Why? (RL) |
| 3 Building Rectangles |
Describe this rectangle:
(CU) |
| 4, 5 Describing Rectangles | Draw a picture of a rectangle that has 12 tiles and 4 columns. (CU) |
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6 Picturing Rectangles Assessment | How would you describe a rectangle? (CU, MC) |
Investigation 3: Fractions of Geometric Shapes
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1,2 Halves of Rectangles and Solids
Assessment | What is a half? (SP) |
| 3,4,5 Cutting Congruent Halves | How do you know that your shape can be cut in congruent halves? (SP, RL) |
| 6 Fraction Flags | How are the flags designed so they are half one color and half another? (SP, MC) |
| 7,8 Fourths and Thirds of Rectangles (excursion) | What does thirds mean? (SP, CU) |
Investigation4: Symmetry
| 1,2 Symmetrical Designs | Name something in the classroom that is symmetrical. Why is it? (SP, CU) |
| 3,4 Reflecting Blocks and Tiles | What would happen to the symmetry of your design if you moved the mirror? (SP) |
| 5,6 Paper Folding and Cutting | How could you prove this shape is symmetrical? (RL) |
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7 Symmetrical Pictures Assessment | How is your picture symmetrical? (SP, CU) |
Putting Together and Taking Apart
Investigation 1: Combining and Separating
| 1 Introducing Combining Situations | What does combining mean? (CU) |
| 2 Introducing Separating Situations | What does separating mean? (CU) |
| 3,4 Making Sense of Addition and Subtraction | Is this problem a combining or separating problem? How do you know? (RL) |
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5,6 Writing Stories for Numerical Problems Assessment | Write a story problem for 12 + 6 = (SP) |
Investigation 2: Working with 100
| 1 Exploring the 100 Chart | What are some multiples of 5? (SP) |
| 2 Games on the 100 Chart | How many more cubes do I need to make 50 if I am on 39? (SP) |
| 3,4 Working with 100 | How far are you from ___ cubes? How can you find out? (SP, RL) |
| 5,6 Collect $1 | What is the least number of coins you could have to equal $1? (SP, RL) |
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7 How Many Paper Clips? Assessment | What strategies did you use to count the paper clips? (RL) |
Investigation 3: Finding the Missing Part
| 1 Parts and Wholes | How can you find the missing part? (SP,RL) |
| 2 Problems with a Missing Part | What story could we write for 26 - ____ = 19? (SP) |
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3,4,5 Separating and Combining Choices Assessment | Can we solve this problem with addition and subtraction? (SP, CU) |
Investigation 4: Adding Up to 100
| 1 Emma’s Animals | How do you keep track of the amounts to be added? (CU) |
| 2 Ways to Make 100 | Write a number string with 4 numbers equal to 100. (SP,CU) |
| 3,4 Stories About 100 |
What is a story for 54 + 23 =? (SP) |
Investigation 5: Addition and Subtraction Strategies
| 1 Introducing Comparing Situations | What is a strategy you use to compare two amounts? (RL, CU) |
| 2, 3 Capture 5 | How far did you move? How do you know? (RL) |
| 4,5 Strategies for Combining | What is a strategy you use for combining amounts? (CU) |
| 6 Capture 5 Strategies | What cards would you use to get to get to 45 from 14? (MC, SP) |
| 7 Strategies for Separating | Can you explain ___’s strategy? (RL, CU) |
| 8 How Far? Assessment | What was easy or difficult about today’s lesson? Why? (CU) |
How Long? How Far?
Investigation 1: Comparing Lengths
| 1 Scavenger Hunt | How did you measure the long lengths? Why? (SP, RL) |
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2,3,4 A Scavenger Hunt Choice Time Assessment | What did you notice as you used the blue and yellow strips? (CU, MC) |
| 5,6,7 Choices About Measurement | How did you count the cubes used to measure the distance? (SP, CU) |
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8 Measuring Our Classroom Assessment | What tool did you choose to measure the classroom? Did you get an accurate measurement? Why or Why not? (SP, RL) |
Investigation 2: Paths and Geo-Logo
| 1 Walking, Visualizing, and Representing Paths | Describe your path. (CU) |
| 2,3 Investigating Turns | Did you reach the baby turtle without running out of energy? Why or why not? (SP, RL) |
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4,5 Measuring Paths
Assessment |
Do turn amounts stay the same even thought the step-size changes? Why or why
not? (SP,RL)
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6,7,8 Moving on a Grid
Assessment | What strategy did you use to plan Tina the Turtle’s trip? Why? (RL, CU) |
| Ongoing Excursion: Geo-Logo : Shapes and Pictures |
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Third Grade Critical Questions