few_shots: 
Example 1:
Concept/skill: 
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.

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.


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

Example 2:
Concept/skill: 
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.

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} $

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Example 3:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

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?


Answer: 
Yes. 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.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_pos_0

5
standard_description: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
problem_activity: Activity
The purpose of this activity is for students to compare two different proportional relationships represented in different ways using the skills they have worked on over the past three lessons. Working in groups, students compare the relationships, responding to questions about their rate of change, which rate of change is higher, and one other situation-based question. Groups make a visual display for their problem set to explain each of their responses and convince others of their accuracy.
Identify groups using a variety of representations to share during the Activity Synthesis.
Launch
Remind students that in previous lessons they identified representations of and created representations for a single proportional relationship. In this activity, they will consider representations of two
different
proportional relationships and make comparisons between them.
Arrange students in groups of 2–3. Assign to each group (or ask groups to choose) one of the three question sets. Tell groups that they will make a visual display for their responses to the questions. The display should clearly demonstrate their reasoning and use multiple representations in order to be convincing. Let them know that there will be a gallery walk when they finish for the rest of the class to inspect their solutions’ accuracy.
If time allows, ask groups to complete all three problems and make a visual display for just one.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills in problem-solving, chunk this task into more manageable parts. For example, present one question at a time.
Supports accessibility for: Memory; Organization
Student Facing
Elena babysits her neighbor’s children. Her earnings are given by the equation
\(y=8.40x\)
, where
\(x\)
represents the number of hours she worked and
\(y\)
represents the amount of money she earned.
Jada earns
$
7 per hour mowing her neighbors’ lawns.
Who makes more money after working 12 hours? How much more do they make? Explain your reasoning by creating a graph or a table.
What is the rate of change for each situation and what does it mean?
Using your graph or table, determine how long it would take each person to earn
$
150.
Clare and Han have summer jobs stuffing envelopes for two different companies.
Han earns
$
15 for every 300 ​​​​​envelopes he finishes.
Clare’s earnings can be seen in the table.
| number of                             envelopes | money                             in dollars |
|-------------------------------------------------|----------------------------------------------|
|                       400                       |                      40                      |
|                       900                       |                      90                      |
By creating a graph, show how much money each person makes after stuffing 1,500 envelopes.
What is the rate of change for each situation and what does it mean?
Using your graph, determine how much more money one person makes relative to the other after stuffing 1,500 envelopes.  Explain or show your reasoning.
Tyler plans to start a lemonade stand and is trying to perfect his recipe for lemonade. He wants to make sure the recipe doesn’t use too much lemonade mix (lemon juice and sugar) but still tastes good.
Lemonade Recipe 1 is given by the equation
\(y=4x\)
where
\(x\)
represents the amount of lemonade mix in cups and
\(y\)
represents the amount of water in cups.
Lemonade Recipe 2 is given in the table.
| lemonade mix (cups) | water (cups) |
|---------------------|--------------|
|         10          |      50      |
|         13          |      65      |
|         21          |     105      |
If Tyler had 16 cups of lemonade mix, how many cups of water would he need for each recipe? Explain your reasoning by creating a graph or a table.
What is the rate of change for each situation and what does it mean?
Tyler has a 5-gallon jug (which holds 80 cups) to use for his lemonade stand and 16 cups of lemonade mix. Which lemonade recipe should he use? Explain or show your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Han and Clare are still stuffing envelopes. Han can stuff 20 envelopes in a minute, and Clare can stuff 10 envelopes in a minute. They start working together on a pile of 1,000 envelopes.
How long does it take them to finish the pile?
Who earns more money?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Some students may confuse the values for the rate of change of a situation. For example, Lemonade Recipe 1's equation,
\(y=4x\)
, shows that the rate of change is 4 cups of water per cup of lemonade mix. Students may switch these values and think that the rate of change is 4 cups lemonade mix per cup of water. Ask students who do this to explain where in the original representations they see the rate of change. Students may need to list a few values or sketch a graph in order to see their mix-up between the two quantities.
Activity Synthesis
Begin with a gallery walk for students to see how other groups answered the same set of questions they did and how students answered questions about the other two contexts.
Invite groups to share the strategies they used with the various representations. Consider asking groups the following questions:
“What representations did you choose to answer the questions? Why did you pick them?”
“What representation did you not use? Why?”
“How did you decide what scale to use when you made your graph?”
“Now that you have seen the work of other groups, is there anything about your display you would change if you could?”
Representing and Conversing: MLR7 Compare and Connect.
During the gallery walk, invite students to discuss “what is the same and what is different?” about the representations on the posters and then share with the whole class. Look for opportunities to highlight representations that helped students answer the questions and decide which scales to use for the graph. This will help students make connections and describe the usefulness of each type of representation.
Design Principle(s): Optimize output


aligns: no