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: Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.

Extend the domain of trigonometric functions using the unit circle.

Construct and compare linear and exponential models and solve problems.

Use functions to model relationships between quantities.

Interpret expressions for functions in terms of the situation they model.

Interpret functions that arise in applications in terms of the context.

Prove and apply trigonometric identities.

Build new functions from existing functions.

Understand the concept of a function and use function notation.

Build a function that models a relationship between two quantities.

Analyze functions using different representations.
problem_activity: Warm-up
In this warm-up, students are prompted to compare function values. To do so, they need to interpret statements in function notation and connect their interpretations to the graph of the function.
Previously, students recognized that if a point with coordinates
\((2,20)\)
is on the graph of a function, the 2 is an input and the 20 is a corresponding output. Here, they begin to see the second value in a coordinate pair more abstractly, as
\(f(2)\)
when the input is 2, or as
\(f(4)\)
when the input is 4.
Launch
Give students 1–2 minutes of quiet think time. Follow with a whole-class discussion.
Some students might be unfamiliar with drones. If needed, give a brief explanation of what they are.
Student Facing
[IMG]
Here is a graph that represents function
\(f\)
, which gives the height of a drone, in meters,
\(t\)
seconds after it leaves the ground.
[IMG]
Decide which function value is greater.
\(f(0)\)
or
\(f(4)\)
\(f(2)\)
or
\(f(5)\)
\(f(3)\)
or
\(f(7)\)
\(f(t)\)
or
\(f(t+1)\)
Student Response
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Activity Synthesis
Invite students to share how they compared each pair of outputs. If not mentioned in students’ explanations, point out that for each pair, what we are comparing are the vertical values of the points on the graph at different horizontal values. Even though the statements don’t tell us the values of, say
\(f(3)\)
and
\(f(7)\)
, and the vertical axis shows no scale, we can tell from the graph that the function has a greater value when
\(t\)
is 3 than when
\(t\)
is 7.
Tell students that the coordinates
\((0, f(0))\)
represent the starting point of the drone. Ask students, “What are the coordinates of the points when the drone starts leveling off? When it starts to descend? When it lands?” (
\((2, f(2)), (5,f(5))\)
, and
\((7,f(7))\)
, respectively.)
Highlight that the coordinates of each point on a graph of a function are
\((x, f(x))\)
.
Discuss with students how they compared
\(f(t)\)
and
\(f(t+1)\)
(in the last question). Make sure students see that the
\(f(t+1)\)
could be less than, equal to, or greater than
\(f(t)\)
, depending on the value of
\(t\)
.
If
\(t\)
is 2, then
\(t+1\)
is 3. From the graph, we can see that
\(f(2)\)
is equal to
\(f(3)\)
because the graph has the same vertical value when
\(t\)
is 2 and 3.
If
\(t\)
is 5, then
\(t+1\)
is 6. From the graph, we can see that
\(f(5)\)
is greater than
\(f(6)\)
because the graph has a greater vertical value when
\(t\)
is 5 than when
\(t\)
is 6.


correct_option_index: 9