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

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

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

Understand place value.

Extend the counting sequence.

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.

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.

Understand the place value system.
problem_activity: Narrative
The purpose of this activity is for students to compose and decompose numbers 11–19 as 10 ones and some more ones. Students work with groups of 11–19 objects to represent a context about students in a classroom where there is room for 10 students to sit at a table and the rest of the students sit on a rug. To solve the problem, students may count the total number of objects and then find a group of 10 or they may start by putting 10 objects at the table and see how many cubes are left on the rug and count all, count on, or know the total without counting. They record the two groups and the total by filling in equations.
Students work with multiple collections of 11–19 objects. They can be given access to a variety of collections of objects to choose from and then switch collections with other groups.
MLR8 Discussion Supports.
Invite students to act out the scenario. Listen for and clarify any questions about the context.
Advances: Speaking, Representing
Action and Expression. Develop Expression and Communication:
Give students access to 10-frames to help them figure out the number of students that will be sitting at the table and rug.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Required Materials
Materials to Gather
Collections of objects
Required Preparation
Each group of 2 needs access to at least 2 collections of 11–19 objects.
Launch
Groups of 2
Give each group of students access to collections of 11–19 objects.
“We are going to pretend that the objects in the collection are students.”
“The students will either sit at the table or on the rug.”
Display the image.
“All of the students want to sit at the table. How many of the students can sit at the table?” (10 students)
1 minute: independent work time
“10 students can sit at the table. The students who do not fit at the table will sit on the rug.”
“Work with your partner to figure out how many students will sit at the table, how many will sit on the rug, and how many students there are altogether. Fill in an equation for each bag of objects.”
Activity
7 minutes: partner work time
Student Facing
[IMG]
[IMG]
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
[IMG]
[IMG]
\(\underline{\hspace{1.1 cm}}\)
\(+\)
\(\underline{\hspace{1.1 cm}}\)
\(= \phantom{la} \underline{\hspace{1.1 cm}}\)
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
“The collection Jada is working with has 14 objects. She showed 10 students sitting at the table. How many do you think will be still on the rug? Why do you think that?” (4, 10 and 4 is 14)


correct_option_index: 1