few_shots: Example:
Problem/activity:
Stage 1: Money
Required Preparation
Materials to Copy
Blackline Masters
Would You Rather Stage 1 Spinner
Would You Rather Stage 1 Recording Sheet

Narrative
The first partner spins to get a group of coins. They write a question that compares the amount they spun to a different group of coins that they make up.


Mathematical concept/skill options: 
A. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
B. Represent and interpret data.
C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
D. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
E. Describe and compare measurable attributes.
F. Geometric measurement: understand concepts of angle and measure angles.
G. Convert like measurement units within a given measurement system.
H. Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
I. Measure and estimate lengths in standard units.
J. Classify objects and count the number of objects in each category.
K. Tell and write time.
L. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
M. Measure lengths indirectly and by iterating length units.
N. Work with time and money.
O. Relate addition and subtraction to length.


Your response:
Thought: In this problem, students work with money in the form of coins.
Answer: N

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_center_000269

2
options: Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Use equivalent fractions as a strategy to add and subtract fractions.
problem_activity: Narrative
This activity prompts students to use number lines to illustrate the decomposition of a fraction into sums of other fractions, reinforcing their work from an earlier lesson. Along the way, students recognize that one way to decompose a fraction greater than 1 is to write it as a sum of a whole number and a fraction less than 1. This insight prepares students to interpret and write mixed numbers in later activities.
Action and Expression: Develop Expression and Communication
. Provide access to colored pencils. Invite students to trace or draw each “jump” with a different color. Then invite students to circle or write out each addend in the corresponding color.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing, Organization
Launch
Display or draw this number line:
[IMG]
“What number does the point describe?” (8)
“What do you think the ‘jumps’ represent?” (The numbers that are put together to go from 0 to 8)
“What equations can we write to represent the combination of jumps?” (
\(6 + 2 =8\)
or
\(2 + 6 = 8\)
)
“Let’s look at the jumps on some other number lines and see what they may represent.”
Activity
Groups of 2
“Work independently on the activity for a few minutes. Afterwards, share your responses with your partner.”
5–7 minutes: independent work time
2 minutes: partner discussion
Student Facing
On each number line, draw two “jumps” to show how to use sixths to make a sum of
\(\frac{8}{6}\)
. Then, write an equation to represent each combination of jumps.
[IMG]
[IMG]
Noah draws the following diagram and writes:
\(\frac{8}{6} = \frac{6}{6} + \frac{2}{6}\)
and
\(\frac{8}{6} = 1 + \frac{2}{6}\)
. Which equation is correct? Explain your reasoning.
[IMG]
On each number line, draw “jumps” to show how to use thirds to make a sum of
\(\frac{7}{3}\)
. Then, write an equation to represent each combination of jumps.
[IMG]
[IMG]
Write
\(\frac{7}{3}\)
as a sum of a whole number and a fraction.
Student Response
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Advancing Student Thinking
Students may not make a connection between the fractions in the problems and the number lines because the latter show no fractional labels. Consider asking students to label the number line to show fractions or asking, “Where do you think
\(\frac{1}{6}\)
would be labeled on this number line?”
Activity Synthesis
Invite students to share their equations. Record them for all to see.
Focus the discussion on part b: writing
\(\frac{7}{3}\)
as a sum of a whole number and a fraction. Students are likely to write
\(1 + \frac{4}{3}\)
and
\(2 + \frac{1}{3}\)
.
Explain that
\(2 + \frac{1}{3}\)
can be written as
\(2\frac{1}{3}\)
, which we call a
mixed number
. This number is equivalent to
\(\frac{7}{3}\)
.
“Why might it be called a mixed number?” (It is a mix of a whole number and a fraction.)


correct_option_index: 1