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.


Standard options: 
A. Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.
Answer: B

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?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
problem_activity: Narrative
The purpose of this activity is for students to practice generating two different patterns from two different rules and observe and quantify relationships between corresponding terms. Both sets of rules generate patterns that have the same relationships between corresponding terms. Each of Priya’s terms is 3 times greater than each of Jada’s corresponding terms and each of Jada’s terms is
\(\frac{1}{3}\)
of Priya’s corresponding terms.
When students find and explain patterns related rules and relationships, they look for and express regularity in repeated reasoning (MP8).
Launch
Groups of 2
“You and your partner will each complete some problems about patterns independently. After you’re done, discuss your work with your partner.”
Activity
5 minutes: independent work time
3 minutes: partner discussion
“Look back at your work and make any revisions based on what you learned from discussing with your partner.”
1–2 minutes: independent work time
Monitor for students who:
revise their thinking based on partner discussion
use multiplication expressions to represent the relationships between the patterns
Student Facing
Partner A
Use each rule to create a pattern.
Jada’s rule: Start at 0. Keep adding 2.
[IMG]
Priya’s rule: Start at 0. Keep adding 6.
[IMG]
If the patterns continue:
What number will be in Priya’s pattern when Jada’s pattern has 34? Explain or show your reasoning.
What number will be in Jada’s pattern when Priya’s pattern has 120? Explain or show your reasoning.
What relationships do you notice between the numbers in Priya's pattern and the numbers in Jada's pattern?
Partner B
Use each rule to create a pattern.
Jada’s rule: Start at 0. Keep adding 3.
[IMG]
Priya’s rule: Start at 0. Keep adding 9.
[IMG]
If the patterns continue,
What number will be in Priya’s pattern when Jada’s pattern has 54? Explain or show your reasoning.
What number will be in Jada’s pattern when Priya’s pattern has 198? Explain or show your reasoning.
What relationships do you notice between the numbers in Priya’s pattern and the numbers in Jada’s pattern?
Student Response
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Activity Synthesis
Ask previously identified students to share their thinking.
Display completed patterns from both sets of rules.
“How are the patterns from the pairs of rules the same? How are they different?” (Some of the numbers are in all four patterns. Some numbers aren’t in any pattern like 5 and 11. In both sets of rules, Priya’s numbers are 3 times greater than Jada’s numbers and Jada’s numbers are
\(\frac{1}{3}\)
Priya’s numbers.)
“How would you describe the relationship between Priya's pattern and Jada's pattern?” (Priya's numbers are all 3 times as much as Jada's corresponding numbers.)
“What can I multiply the numbers in Priya’s pattern by to get the corresponding numbers in Jada’s pattern?” (
\(\frac{1}{3}\)
, each number in Jada's pattern is
\(\frac{1}{3}\)
the corresponding number in Priya's pattern.)


correct_option_index: 0