Critical Questions for Investigations Grade 3
Mathematical Thinking
Investigation 1: What’s a Hundred?
| 1 How Much is 100? | How did you count to 100? (CU, SP) |
| 2,3 Working with 100 Assessment | Is there a way to double – check our counts? (RL) |
Investigation 2: Doubles and Halves
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1 Pattern Blocks Assessment | What is a strategy for remembering doubles? (SP) |
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2 Strategies for Addition Assessment | What do you notice about the list? (SP, RL) |
| 3,4 Finding Doubles and Halves | Which combinations are you working on and what are your clues? (CU) |
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5,6,7 Doubling with Money Assessment | How did you solve the double problem? (CU, SP) |
Investigation 4: Exploring Odds and Evens
| 1 Adding Odds and Evens | What happens when you add two odd numbers? Why? (RL) |
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2 Odds and Evens on the Calculator Assessment |
Which number split evenly and which don’t? Why? (RL, SP) |
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3 What We’ve Learned About Odds and Evens Assessment | What was easy or hard for you during this unit? (CU) |
Things That Come in Groups
Investigation 1: Things That Come In Groups
| 1 Many Things Come In Groups | How do you know your (partner’s) solution is correct?(RL) |
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2 How Many In Several Groups? Assessment | What is the relationship between addition and multiplication? (CU) |
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3 Writing and Solving Riddles Assessment | What does it mean to multiply? Can you give an example?(CU,RL) |
| 4 Each Orange Had 8 Slices | How did you solve the problems? (CU) |
Investigation 2: Skip Counting and 100 Charts
| 1 Highlighting Multiples In 100 Charts | What patterns do you see? (CU, RL) |
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2 Using the Calculator to Skip Count Assessment | How could you use the calculator to figure which numbers make groups of ___?(SP, RL) |
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3,4 More Practice with Multiples Assessment | How can you use your 100 chart to find the answer to 8 x 4?(SP) |
| 5,6 Discussing Number Patterns | What patterns do you see in the 12’s chart?(CU) |
Investigation 3: Arrays and Skip Counting
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1,2 Arranging Chairs Assessment | What are all the factors of 12? (SP) |
| 3,4 Array Games |
What pairs do you still need to work on? Which do you already know?(CU) |
| 5 The Shapes of Arrays Assessment | How could you write that as a division problem? (SP) |
Investigation 4: The Language of Multiplication and Division
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1,2 Multiply or Divide? Assessment | How many ways can you write a division sentence? Give examples. (SP) |
| 3,4 Writing and Solving Story Problems | What is the relationship between multiplication and division? (CU, RL) |
Investigation 5: Problems with Larger Numbers
| 1 Calculating Savings | What are some patterns you notice?(CU) |
| 2 Many, Many Legs | How many legs would there be on all the four-legged animals? (SP) |
| 3 Data Tables and Line Plots | What does the line plot tell us? (CU) |
| 4 A Riddle with 22 Legs (Assessment) | How did you solve the problem? (SP, CU) |
Flips, Turns and Area
Investigation 1: Motions with Tetrominoes
| 1 Tetrominoes | How can you tell if two shapes are congruent? (SP) |
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2,3 Slides, Flips, and Turns Assessment | What are slides, flips, and turns? (CU) |
| 4 Rectangles with Different Shapes | Are the different shapes for rectangles all “fair”? Why or why not? (RL) |
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5 Final Challenges Assessment | At the Star level, you can’t use flips. Are flips really ever needed? Why? (SP, RL) |
Investigation 2: Finding Area
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1 Triangles and Squares Assessment | When would you need to measure the area of something? (SP) |
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2,3 A Poster of Four-Unit Shapes Assessment | Create a shape with an area of 6 that is not a rectangle. (SP) |
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4,5 Writing About Area Assessment | Calculate the area for a 12-by-5 rectangle? What strategy did you use? (SP, CU) |
From Paces to Feet
Investigation 1: Measuring with Paces and Steps
| 1 Giant Steps and Baby Steps | How do giant steps compare to baby steps? (CU) |
| 2 Pacing and Comparing | What is a pace? How does a pace compare to giant steps and baby steps? (SP, CU) |
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3,4 Robot Directions Assessment | Why do the directions work for some people but not all? (MC) |
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5,6 Finding the Middle-Sized Pace Assessment | How can we find the middle sized pace? (SP) |
Investigation 2: From Paces to Feet
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1 The Need for a Standard Measure Assessment | Why is it important to have a standard measure? (CU, MC) |
| 2 Kids Feet and Adults Feet | What is the typical foot length in our class? (CU) |
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3,4 Measuring Centers Assessment | How do you keep track of the units when you measure? (CU) |
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5 Moving to Metric
Assessment | What could you use to measure centimeters if you didn’t have a ruler? (CU) |
6,7 Metric
Measurement
Assessment | What are some things to remember to measure accurately? (CU) |
Investigation 3: Measuring Projects: Do Our Chairs Fit Us?
1 What’s a Good Fit? | How does collecting and organizing data help us to analyze a situation? (CU, MC) |
2,3 Do Our
Chairs Fit Us? | What is a recommendation you would make based on the data we collected? (CU, RL) |
Landmarks in the 100’s
Investigation 1: Finding Factors
| 1 Skip Counting with Cubes | How do you know if this number “works?” (RL) |
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2,3 Factors of 24, 36, and 48 Assessment | How do you know what comes next? (RL) |
| 4,5 Factors of 100 | How do you know if you have found all the numbers? (RL) |
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6,7 Dividing a Dollar Assessment | How many 20’s are in 100?
How many 4’s are in 100? Prove that you are correct. (RL, MC) |
Investigation 2: Using Landmarks to Solve Problems
| 1,2,3 Moving Beyond 100 Assessment | How did you double-check your counting strategy? (RL) |
| 4 Solving Problems with Money | How did you represent your problem? (CU) |
| 5,6 Real-World Multiplying and Dividing |
What is a problem you created? What did you find? (SP, CU) |
Investigation 3: Constructing a 1000 Chart
| 1 A 1000 Chart | How many more __ do you need? How do you know? (SP,RL) |
| 2,3 Finding Large Quantities Assessment | How far is it from ___ to ___? How did you solve it? (SP,RL) |
Combining and Comparing
Investigation 1: Comparisons with Record Numbers
| 1,2 How Many Children In Your Family? | How far over 100 is your total? How do you know? (SP, RL) |
| 3 More Record Comparisons | What is your strategy for finding the difference? (CU) |
Investigation 2: How Much Heavier or Lighter?
| 1 Weighing Fruits and Vegetables | What is the difference between the starting weight and the second weight? What caused that to happen? (RL, MC, CU) |
| 2 Comparing the Weights Assessment | What would happen to the weight if you left an apple out for a month and then reweighed it? (RL) |
Investigation 3: Adding with Money, Inches and Time
| 1, 2 Heights and Coupons | What strategies did you use to find the sum or difference in the activity? (SP, CU) |
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3 Planning a Party Assessment | What is your strategy for double checking your work? (RL) |
Investigation 4: Working with Hundreds
| 1 Handfuls of Beans |
What does the line plot tell you? (CU, MC) |
| 2 More Handfuls |
See question on pg. 50 “Suppose you can hold 150 beans in your right hand and 217 beans in your left hand…” (SP) |
| 3,4 Hundreds of Paper Clips | Subtract 7 paper clips from 700, the total number of clips of some boxes. How many paper clips are there now? (SP, CU) |
Investigation 5: Calendar Comparisons
| 1 How Much Longer? | How much longer until…? (SP) |
| 2,3 School Days | What method do you use to keep track? (CU) |
Measurement Activities
Investigation 1: Metric Stations
| 1,2 Metric Stations | What are benchmarks for 1 meter, 10 centimeters, 500 grams, 1 kilogram, and 1 liter? |
Investigation 2: Scavenger Hunt
| 1 The Hunt | What kinds of tools are used to measure and what to they do? |
Investigation 3: Metric Olympics
| 1,2 Olympic Games | When is it important to measure exactly and when would an estimate be enough? |
Turtle Paths
Investigation 1: Paths and Lengths of Paths
| 1 Walking Paths |
Draw the following path: (use grid paper) fd6, lt90, fd5 Finish the commands so that it creates a closed shape. (SP) |
| 2 Commanding the Turtle | What was hard/easy about working on the computer today? (CU) |
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3,4 Mazes and Maps Assessment | How did you figure out how far to move the turtle? (SP, RL, CU) |
Investigation 2: Turns in Paths
| 1,2 Turns | Estimate a 30, 60 and 90 degree turn on a piece of paper. (RL) |
| 3 Turns, Turtles, and Triangles | Which turns were particularly hard for you to measure? Why? (CU, RL) |
| 4 Equilateral Triangles Assessment | What is an equilateral triangle? (CU) |
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5,6 Missing Measures Assessment | How did you find the missing lengths and turns? (CU, SP) |
Investigation 3: Paths with the Same Length
| 1,2 The 200 Steps | Is it possible to make a shape of 200 turtle steps with four 90 degree turns that is not a rectangle? (SP, RL, CU) |
| 3,4,5 Facing Problems Assessment | What is perimeter? How could you figure out the perimeter of a rectangle if one side was 4” and the other was 2”? (SP) |
Up and Down the Number Line
Investigation 1: Net Changes
| 1,2 Elevator Trips Up and Down | Is the starting position important? Why or why not? |
| 3,4 Many Ways to Make One Net Change | Explain one strategy you used or just learned to play the game. |
| 5 Thirty Changes | How do you keep track of partial calculations? Is it efficient? Why or why not? |
| 6,7 Missing Information Problems | Does it matter what order your changes are in to get to the total effect? Why or why not? |
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8 Stopping at Many Floors (excursion optional) | What kinds of number combinations make the elevator stop at as many floors as possible? |
Investigation 2: Representing Elevator Trips
| 1 Graphing Elevator Trips | How did you decide what trip each graph represented? |
| 2,3 Repeating Elevator Trips | How can you tell where the elevator starts to repeat? |
| 4 Plus and Minus Graphs | What have you learned about line graphs? |
Investigation 3: Inventing Board Games
| 1 Playing A Board Game | Why is it important to have conventions when creating a number line? |
| 2, 3 Creating a Board Game | What was easy or hard for you during this unit? Why? |
Fair Shares
Investigation 1: Sharing Brownies
| 1, 2 Making Fair Shares Assessment |
Order these fractions from the smallest to the largest. 1/3, ½, 1/6, ¼ (SP) |
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3,4 More Brownies to Share Assessment | Identify the numerator. What is it telling us? 2/3 (CU) |
Investigation 2: Pattern Block Cookies
| 1,2 Making Cookie Shares | What are two ways to make ½? (SP) |
| 3 Comparing Shares Assessment | Prove that ½ is larger than ¼. (RL, CU) |
| 4 The Fraction Cookie Game* | What is a fraction that is equivalent to ½? How do you know? (SP, RL) |
| 5,6 Backward Sharing | Why do you think only an even number of people get shares with halves? (CU, RL, MC) |
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7 Half Yellow
(Optional) | How do you know that exactly half your design is yellow? (RL, CU) |
Investigation 3: Other Things to Share
| 1,2 How Can We Split Balloons? | Share $5.00 equally with a friend. How much would each of you get? (SP, CU, MC) |
| 3 Sharing Many Things | Find 1/3 of 40 beads, to show how many beads each of 3 people could have. (SP, CU) |
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Third Grade Critical Questions