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:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

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

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Describe and compare measurable attributes.

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

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

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

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

Geometric measurement: understand concepts of angle and measure angles.

Measure lengths indirectly and by iterating length units.

Convert like measurement units within a given measurement system.

Relate addition and subtraction to length.

Work with time and money.

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

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

Tell and write time.

Represent and interpret data.

Measure and estimate lengths in standard units.
problem_activity: Narrative
The purpose of this activity is for students to ask and answer questions using their bar graphs from a previous activity. Students work with the group they collected survey data with to create questions that can be answered with their bar graphs. Then students are paired up with a new partner to use these questions to practice solving one- and two-step “how many more” and “how many fewer” problems using information presented in scaled bar graphs (MP2).
MLR8 Discussion Supports.
Prior to solving the problems, invite students to make sense of the bar graphs and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Advances: Speaking, Representing
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group needs the bar graphs they created in the previous activity.
Launch
Groups of 4
“Work with your group to complete these sentences to write questions that could be answered with your bar graph.”
5–7 minutes: small-group work time
Have each group share one of their questions and how they came up with the question.
Activity
Groups of 2
Be sure students have a partner that wasn’t in their group in the previous activity.
“Use your partner's graph to answer the questions your partner wrote. They’ll answer your questions while you’re answering theirs. Then you’ll spend a few minutes checking each other’s work.”
7–10 minutes: partner work time
Have students switch partners again and repeat as time permits.
Student Facing
Write questions that could be answered with your bar graph by completing these sentences.
How many more students liked ___________________________
than ___________________________ ?
How many fewer students liked ___________________________than
___________________________ ?
How many more students liked ___________________________or
___________________________ than ___________________________ ?
Use your partner’s graph to answer their questions. Show or explain your reasoning.
The answers to the questions from ___________________________ ’s graph:
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“What was the most interesting question you answered about a scaled graph?”


correct_option_index: 13