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: Describe and compare measurable attributes.

Tell and write time.

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.

Measure lengths indirectly and by iterating length units.

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

Geometric measurement: understand concepts of angle and measure angles.

Represent and interpret data.

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

Convert like measurement units within a given measurement system.

Work with time and money.

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

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

Relate addition and subtraction to length.

Measure and estimate lengths in standard units.
problem_activity: Narrative
The purpose of this activity is for students to use a bar graph to compare two quantities and describe the methods they use to find the unknown difference. Monitor for students who draw on the graph and describe ways of finding the difference by counting on or counting back. If students draw on their graph or do not discuss both counting methods during the activity, create and display work so that each method can be discussed during the synthesis. The discrete segments of the bar graph are used to elicit these counting methods (MP5), however, some students may use addition or subtraction, including known sums, to find the difference. Encourage these students to connect their methods to the counting methods shared in the synthesis.
MLR8 Discussion Supports.
Provide all students with an opportunity to speak and to practice using comparison statements. Invite students to chorally repeat statements that use “more” and “fewer” in unison 1–2 times.
Advances: Speaking, Listening
Launch
Groups of 2
Display the image (graph with no scale).
“A group of third grade students were asked, ‘What pets do you have?’ Their responses are shown in the bar graph."
"What do you notice about the data in the graph? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Monitor for students to say: “More students have cats than have rabbits,” or wonder, “How many more students have cats than have rabbits?”
Share and record student responses.
If students do not make statements using “more” or “fewer,” display:
“There are more _____ than _____.”
“There are fewer _____ than _____.”
“How could you complete the sentences to make them true statements about the graph?”
1 minute: quiet think time
1 minute: partner discussion
Share responses.
Activity
“You noticed that more students have cats than have rabbits. Your job now is to figure out how many more students have cats than have rabbits. Think about two different ways you can find the answer and record them.”
3–4 minutes: independent work time
2–3 minutes: partner discussion
Monitor for a student who uses a counting on method and a student who uses a counting back method.
Student Facing
A group of third grade students were asked, "What pets do you have?" Their responses are shown in the bar graph.
What do you notice? What do you wonder?
[IMG]
Their responses are also shown in this bar graph.
[IMG]
How many more students have cats than have rabbits? Show two ways to find the difference.
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
Invite previously identified students to share how they found the difference. If methods are only explained verbally, consider asking, “Can you show us on the bar graph how you could count on (or count back) to find how many more?”
Record student methods with an equation. For example, for students who describe counting on, write “8 + 9 = 17.”
"How are their methods similar? How are their methods different?" (One method starts with the smaller number of pets and counts on to the larger number, like adding 9 more. The other starts with the larger number of pets and counts back to the smaller number, like subtracting 9.)


correct_option_index: 7