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.


Your response:
{
  "explanation": "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.


Your response:
{
  "explanation": "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.


Your response:
{
  "explanation": "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 place value.

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

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

Extend the counting sequence.

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

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.

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.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
problem_activity: Narrative
The purpose of this activity is for students to convert from meters to centimeters using the context of a standing broad jump, a common test for physical fitness. Students may multiply by 100 to convert from meters to centimeters or divide by 100 to convert from centimeters to meters. Students should be encouraged to use whatever strategy makes sense to them. Future lessons will focus specifically on conversion from centimeters to meters. Give students access to meter sticks.
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Required Materials
Materials to Gather
Metersticks
Launch
Groups of 2
Display the image from student workbook.
Give students access to meter sticks.
“What do you notice? What do you wonder?” (The girl is jumping. There are numbers on the mat. Did she start where the footprints are? How far did she jump?)
Activity
1–2 minutes: quiet think time
6–8 minutes: partner work time
Monitor for students who:
use their result for Tyler’s jump in centimeters to find his jump in millimeters
use the result in meters to find how far Tyler jumped in millimeters
Student Facing
[IMG]
[IMG]
Here are the distances that each student jumped.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "student"}, {"_attributes": {"scope": "col"}, "_value": "distance"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "Mai"}, {"_value": "1.61 meters"}]}, {"td": [{"_value": "Tyler"}, {"_value": "1.43 meters"}]}, {"td": [{"_value": "Clare"}, {"_value": "1.57 meters"}]}]}]}]}
The average standing broad jump distance for 5th graders is 148 centimeters. Are each of the students in the table below, at, or above the average? Explain or show your reasoning.
The world record for the standing broad jump is 337 centimeters. Jada says that’s more than Mai and Clare jumped combined. Do you agree with Jada? Explain or show your reasoning.
Tyler says his jump sounds more impressive if he reports it in millimeters.
How far is Tyler’s jump in millimeters? What about Mai’s and Clare’s jumps?
Which unit do you think is best for reporting the jumps? Explain your reasoning.
Student Response
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Advancing Student Thinking
If students do not know the relationship between millimeters, centimeters, and meters, show them a meter stick and ask “How can you use the meter stick to figure out how many millimeters are in 1 meter?”
Activity Synthesis
Display the expression:
\(1.43 \times 100\)
.
“How does this expression represent Tyler’s jump in centimeters?” (There are 100 centimeters in a meter.)
Invite students to share how they found Tyler’s jump in millimeters.
Display the expression:
\((1.43 \times 100) \times 10\)
.
“In what unit of measurement does this expression represent Tyler's jump? How do you know?” (It represents Tyler’s jump in millimeters. There are 10 millimeters in a centimeter and
\(1.43\times100\)
represents the centimeters, so if we multiply the number of centimeters by 10, we will get the number of millimeters.)
Display the expression:
\(1.43 \times 1,\!000\)
.
“How does this expression represent Tyler’s jump in millimeters?” (There are 1,000 millimeters in a meter so I have to multiply by 1,000 to get millimeters from meters.)
Display the equation:
\(1.43 \times 1,\!000 = (1.43 \times 100) \times 10\)
.
Invite students to share which unit they prefer to express the distances that the students jumped.
“It’s important to choose a unit that makes sense to you.”


correct_option_index: 7