few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. 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.
B. 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.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. 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.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Measure lengths indirectly and by iterating length units.

Classify objects and count the number of objects in each category.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Describe and compare measurable attributes.

Work with time and money.

Tell and write time.

Relate addition and subtraction to length.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Geometric measurement: understand concepts of angle and measure angles.

Represent and interpret data.

Convert like measurement units within a given measurement system.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Measure and estimate lengths in standard units.
problem_activity: Narrative
The purpose of this activity is for students to measure lengths using a ruler that is marked with half inches and quarter inches. Building on their understanding of equivalent fractions, students recognize that lengths that line up with a half-inch mark can be read as one-half of an inch or two-fourths of an inch. They also recognize that lengths that are whole numbers of inches can be expressed as fractions.
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Required Materials
Materials to Gather
Materials from a previous activity
Rulers (inches)
Required Preparation
Each student needs a ruler marked with half inches and quarter inches from the warm-up.
Launch
Groups of 2
Display the problem.
“Think about how Kiran and Jada record the length of the worm. Use the ruler to explain how both of their measurements make sense.”
1 minute: quiet think time
2–3 minutes: partner discussion
Monitor for students that say they both make sense because
\(4\frac{1}{2}\)
is equivalent to
\(4\frac{2}{4}\)
and select them to share their responses.
Make sure each student has a ruler marked with half inches and quarter inches from the previous activity.
Activity
“Now, work with your partner to measure the length of some worms. Some lengths can be recorded in more than one way. Be ready to explain how you recorded each length.”
3–5 minutes: partner work time
Student Facing
Kiran and Jada are discussing the length of a worm.
[IMG]
[IMG]
Kiran says that the worm is
\(4\frac{2}{4}\)
inches long.
Jada says that the worm is
\(4\frac{1}{2}\)
inches long.
Use the ruler to explain how both of their measurements are correct.
Measure the length of the following worms.
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
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Advancing Student Thinking
If students start measuring from the edge of their ruler instead of from 0, consider asking:
“In the image for the first problem, how is the ruler lined up to the worm?”
“Why does it make sense to not line up the left end of the ruler with the left end of the worm?”
Activity Synthesis
Invite students to share how they recorded their measurements and why they chose to record them in the way they did.
“Let’s think more about the first worm you measured. What are all the ways that we could record its length?” (4 inches.
\(\frac{8}{2}\)
inches.
\(\frac{16}{4}\)
inches.)
“What are all the ways that we could record the length of the last worm?” (
\(3\frac{1}{2}\)
inches.
\(3\frac{2}{4}\)
inches.
\(\frac{7}{2}\)
inches.
\(\frac{14}{4}\)
inches.)
“We can use different numbers to describe the same length because the numbers are equivalent.”


correct_option_index: 11