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.
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K

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3

fl_problem_000674

5
options: Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Rewrite rational expressions.

Understand solving equations as a process of reasoning and explain the reasoning.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Use the four operations with whole numbers to solve problems.

Solve systems of equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Understand the connections between proportional relationships, lines, and linear equations.

Use properties of operations to generate equivalent expressions.

Work with equal groups of objects to gain foundations for multiplication.

Add and subtract within 20.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Use polynomial identities to solve problems.

Represent and solve problems involving multiplication and division.

Reason about and solve one-variable equations and inequalities.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand and apply properties of operations and the relationship between addition and subtraction.

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

Solve equations and inequalities in one variable.

Analyze patterns and relationships.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Generate and analyze patterns.

Multiply and divide within 100.

Represent and solve problems involving addition and subtraction.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.
problem_activity: Narrative
The goal of this activity is for students to examine different ways to write the product of a three-digit number and a two-digit number as a sum of partial products. Students match sets of partial products which can be put together to make the full product. Students are provided blank diagrams, familiar from the previous lesson, that they may choose to use to support their reasoning. In the activity synthesis, students relate the expressions and diagrams to equations to prepare them to analyze symbolic notation for partial products in the next activity.
When students relate partial products and diagrams to the product
\(245 \times 35\)
they look for and identify structure (MP7).
MLR8 Discussion Supports.
Display the following sentence frame to support small-group discussion: “I noticed _____ , so I matched . . . .” Encourage students to challenge each other when they disagree.
Advances: Speaking, Conversing
Required Materials
Materials to Copy
Partial Product Expressions
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Display first image from student book.
“What product does this rectangle represent?” (
\(245 \times 35\)
)
“Today, you are going to take turns with your partner picking expressions that can be added together to give the product
\(245 \times 35\)
. You can use the diagrams to explain your reasoning, if they are helpful.”
Activity
10 minutes: partner work time
Monitor for students who:
use the diagram to determine which expressions they will use.
look at the expressions and think about how they could be used to find the full product.
compute the full product in different ways.
Student Facing
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Take turns picking out a set of expressions that are equal to
\(245 \times 35\)
when added together. Use the diagrams if they are helpful.
Explain how you know the sum of your expressions is equal to
\(245 \times 35\)
.
What is the value of
\(245 \times 35\)
? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students do not choose correct expressions to represent a sum that is equal to
\(245 \times 35\)
, refer to one of the empty boxes in the diagram and ask, “Which multiplication expression represents this partial product?”
Activity Synthesis
Invite previously selected students to share their strategies. As students share, record their reasoning with equations.
Display:
\(245 \times 30 + 245 \times 5  = 245 \times 35\)
“How do you know this equation is true?” (I can put the 30 and 5 together since they are both multiplied by 245. I see that
\(245 \times 30\)
is the top part of the diagram and
\(245 \times 5\)
is the bottom part. Together that’s the whole diagram.)


correct_option_index: 23