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: Understand the place value system.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Work with numbers 11–19 to gain foundations for place value.

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.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Extend the counting sequence.

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.
problem_activity: Narrative
In this activity, students recall what they know about division from grade 3. The context allows students to connect lived experiences to the math of the activity. By inviting students to consider treats that they enjoy in their homes or neighborhoods, they share experiences and foster connections that build community.
The first question gives students an opportunity to co-craft mathematical questions based on a situation before answering a question based on a division equation. Students divide a two-digit number by a one-digit divisor, as they did in grade 3, in a way that makes sense to them. The activity synthesis highlights different representations students made and relates them to the situation. The term
dividend
is re-introduced in this lesson to describe a number being divided into equal groups.
This activity uses
MLR5 Co-craft Questions
. Advances: writing, reading, representing
Action and Expression: Develop Expression and Communication.
Give students access to concrete manipulatives (connecting cubes, counters, or square tiles) and grid paper. Invite students to use these to act out or draw
\(84 \div 7\)
.
Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 2
“What are some of your favorite treats or snacks from home?”
30 seconds: quiet think time
1 minute: partner discussion
MLR 5: Co-craft Questions
Display the opening paragraph and the first question.
“Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“How are these questions alike?” (The questions involve multiplying or dividing.) “How are they different?” (The questions can be answered using different operations.)
“Let’s look at the next question in the activity.”
Activity
3–4 minutes: quiet work time
Student Facing
Diego’s aunt is buying paletas, which are ice pops, for a class party. At the local market, paletas come in different flavors. She buys the same number of paletas of each flavor.
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What mathematical questions can we ask about this situation?
Here is an equation:
\(84 \div 7 = {?}\)
In the situation about the class party, what questions could the equation represent?
Find the answer to one of the questions you wrote. Show your reasoning.
Student Response
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Advancing Student Thinking
If students are unsure how to write a division question for
\(84 \div 7\)
, consider asking:
“If you were to act out the meaning of this expression, what would you do?”
“If you were to explain its meaning, what would you say?”
“In what type of situations would these types of actions take place?”
Activity Synthesis
Display two questions that students wrote for the equation
\(84 \div 7 = {?}\)
.
“What does the 84 represent in both problems?” (The amount being divided into equal groups.)
“In mathematics, the number being divided is known as the
dividend
.”
Invite students to share their strategies for the last question. Highlight strategies that show equal-size groups and reasoning that relates multiplication and division.


correct_option_index: 5