Fifth Grade Critical Questions
1
Critical Questions for Investigations Grade 5
Picturing Polygons
Investigation 1: Identifying Polygons
1 Is It a Polygon?
What attributes make a figure a polygon? (SP)
2 Making Polygons
Name and describe one polygon with more than 4 sides. (CU, SP)
3 Polygon Pictures
With
Coordinate Geometry
Assessment
List the ordered pairs of a 4-point shape drawn on a coordinate
grid. (CU)
4 Coordinate Geometry
With Geo-Logo
Draw a polygon using 5 points on a coordinate grid and list the
ordered pairs. (CU, SP)
Investigation 2: Triangles and Quadrilaterals
1,2,3 Sorting Polygons
Assessment
Complete this statement: “All triangles…” (CU, MC)
4,5 Making Shapes
That Follow Rules*
Is it impossible for a triangle to have two right angles? Explain
why or why not? (CU, RL)
6,7 Using Move and
Turn Commands
Assessment
Explain the difference between turns and angles. (CU)
8 Finding Angle Sizes
Assessment
Draw a shape with a 90 degree angle and a shape with a 45
degree angle. (SP, CU)
9 Angles and Turns
Together
What do you know about 45 degree angles and 60 degree
angles? (CU)
Investigation 3: Perimeter and Area
Changing Gardens
What is area? What is perimeter?
Perimeter
How are area and perimeter related?
Spaghetti and
Meatballs for All
What did you notice about the areas and perimeters of the
shapes you made?
Fifth Grade Critical Questions
2
Name That Portion
Investigation 1: Exploring Percents and Fractions
1 Connecting Fractions,
Decimals, and Percents
How are fractions, decimals, and percents related? (CU, RL)
2 Percent Grid Patterns
Explain what percent is. Use pictures, words, and/or numbers (CU)
3,4 Fraction and
Percent Grids
What strategy would you use to find the equivalent percent for
2/5? (SP, RL)
5,6 Percent Equivalent
Strips
Assessment
Order from smallest to largest the following fractions: 7/10, 1/3,
½. How do you know? (SP, RL)
7 Fraction and Percent
Problems
Assessment
Explain what was the most difficult problem for you on SS 9 and
why. (CU)
Investigation 2: Models for Fractions
1,2 Fractions on Clocks How are clock fractions helpful for learning about fractions? (CU,
MC)
3 Fraction Strips
Assessment
Change the following equation into a subtraction problem. 1/2+
1/6 = 2/3
You may use the fraction strips. (SP)
4,5 Fraction Tracks
Would you put a halfway point on the 5’s line? Why or why not?
(RL, CU)
6 The Fraction Track
Game
If you draw an 8/10 card what two moves could you make? (SP,
RL)
7,8 Fraction Games
What is the most difficult game? Why? (CU, RL)
9 Problems with
Fractions
What strategy did you use most on SS #17? (SP)
Investigation 2: Exploring Decimals
1 Interpreting Decimals Complete the following: I learned…or I feel… (CU)
2 Decimals on Grids
Assessment
0.2, 0.02, 0.20 Which is worth the least and why? (CU)
3,4 Decimal Games
Assessment
Which game did you find the easiest and why? (CU)
5,6 Fractions to
Decimals
0.255 and 0.1555555
Which is greater? How do you know? (CU, RL)
7 Fraction, Percent,
and Decimal Problems
Assessment
Explain what was the most difficult problem on SS 23 and why.
(CU, RL)
8 Comparing Fractional
Amounts
Assessment
Which portions did you find the easiest to understand and use –
fractions, decimals, or percents? Why? (RL, MC, CU)
Fifth Grade Critical Questions
3
Building on Numbers You Know
Investigation 1: Exploring Distance Between Numbers
1 Reasoning About
Multiples
How can you tell how many times you have skip counted a number? (SP)
2 Counting Puzzles
Note: Include estimation
in all possible activities.
How do you determine which numbers we can count by between two
numbers? (SP, RL)
3,4 Exploring Patterns of
Multiples
How can you find multiples of a number? (SP)
5 Multiple Towers
Assessment
How can multiple towers help us with multiplication and division? (RL)
6,7 The Digits Game
How can you use the digits of a number to raise and lower a value?
(RL)
8 Subtraction Strategies
Assessment
What are 2 strategies you use to subtract? (SP)
Investigation 2: Multiplication and Division Situations
1,2 Multiplication and
Division Strategies
Assessment
What strategies do you have for solving 2-digit multiplication problems? (SP)
3 Division Strategies
What strategies do you use to divide large numbers in to equal groups? (SP)
4 What Should We Do
with the Extras?
Assessment
What is a situation where you would need to divide? What would you do with
the extras? (SP, RL)
5,6 Relating
Multiplication to Division
How are multiplication and division related? (CU)
Investigation 3: Ways to Multiply and Divide
1,2,3 Multiplication
Clusters
How can you use simple multiplication problems to help you solve more
challenging ones? (MC, SP)
4,5,6 Division Clusters
Assessment
How can multiplication help you solve division problems? (MC, SP)
7,8,9 How Did I Solve It?
What are two or more ways to solve multiplication and division problems? (SP)
10 Ways to Multiply and
Divide
Assessment
I learned… (CU)
Fifth Grade Critical Questions
4
Prime Time
Investigation 1: The Factor Game
1.1Playing the Factor
Game
1.2 Playing to Win
the Factor Game
What did your analysis of the factor game tell you about prime
numbers?
Investigation 2: The Product Game
2.1 Playing the
Product Game
2.2 Make Your Own
Product Game
2.3 Classifying
Numbers
Using the words
factor, multiple and divisible by
, write as many
statements as you can about this mathematical sentence:
4 x 7 = 28
Investigation 3: Factor Pairs
3.1 Arranging Space
3.2Finding Patterns
3.3 Reasoning with
Odd and even
Numbers
How can you tell if a number is divisible by 2? By 5? By 10?
Divisibility Games in Nimble with Numbers 4-5 pg. 98 – 101.
Investigation 4: Common Factors and Multiples
4.1 Riding Ferris
Wheels
4.2 Looking at Locust
Cycle
4.3 Planning a Picnic
Describe how you can find the common multiples for two numbers.
Investigation 4: Factorizations
5.1 Searching for
Factor Strings
5.2 Finding the
Longest Factor String
5.3 Using Prime
Factorizations
How can you use the prime factorization of two numbers to find
their common multiples?
Fifth Grade Critical Questions
5
Data About Us
Investigation 1: The Factor Game
1.1 Organizing Your
Data
1.2 Interpreting Graphs
1.3 Identifying the
Mode & Range
1.4 Identifying the
Mean
1.5 Experimenting with
the Median
What does the median tell you about a set of data?
Investigation 2: Types of Data
2.1 Category and
Number Questions
2.2 Counting Pets
How would you explain what categorical and numerical data are to a
classmate who missed this investigation?
Investigation 3: Using Graphs to Group Data
3.1 Traveling to School
3.2 Jumping Rope
Numerical data can be displayed using more than one kind of graph. How
do you decide when to use a line plot, bar graphs or stem and leaf plots?
Explain your reasoning.
Investigation 4: Coordinate Graphs
4.1 Relating Height to
Arm Span
4.2 Relating Travel
Time to Distance
When you make a coordinate graph of data pairs, what do you consider
when deciding what scale to use on each axis?
Investigation 4: What Do We Mean By
Mean
?
5.1 Evening Things Out
5.2Finding the Mean
5.3 Data with the Same
Mean
5.4 Using Your Class’s
Data
5.5 Watching Movies
You have used three measures of center: the mean, the median, and the
mode.
Why do you suppose these are called “measures of center”? What does
each tell you about a set of data?
Why might people prefer to use the median instead of the mean?
Fifth Grade Critical Questions
6
Bits and Pieces I
Investigation 1: Fundraising Fractions
1.1 Fund Raising
Fractions
1.2 Using Fraction Strips
Folding the fractions in
1.2 takes most of the
period.
1.3 Comparing Classes
1.4 Exceeding the Goal
1.5 Using Symbolic Form
Save fraction strips from
Lab sheet 1.5 for future
lessons.
What do the numerator and denominator of a fraction tell you?
Investigation 2: Comparing Fractions
2.1 Comparing Notes
Finding Equivalent
Fractions
Making a Number
Line
2.4 Comparing Fractions
to Benchmarks
How can you decide whether a given fraction is closed to 0, 1/2, or 1?
Investigation 3: Cooking with Fractions
3.1 Cooking with
Fractions
3.2 Baking Brownies
How can square models help you decide which of two fractions is larger?
Investigation 4: From Fractions to Decimals
4.1 Designing a Garden
4.2 Making Smaller Parts
4.3 Using Decimal
Benchmarks
4.4 Playing Distinguishing
Digits
When comparing two decimals, how can you decide which decimal represents a
larger number?
Investigation 4: Measuring Parallelograms
5.1 Choosing the Best
5.2 Writing Fractions as
Decimal
5.3 Moving From
Fractions to
Decimals
Describe how to find a decimal equivalent to a given fraction. How can you check
your strategy to see that it works?
Investigation 2: One Out of One Hundred
6.1 It’s Raining Cats
6.2 Dealing with
Discounts
6.3 Changing Forms
6.4 It’s Raining Cats &
Dogs
Describe how you can change a percent to a decimal and to a fraction.
Describe how you can change a fraction to a percent.
Describe how you can change a decimal to a percent.
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