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: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
problem_activity: Activity
In this first part of the project, students make sense of the task at hand and determine what they need to know and do to find the most economical shipping box combination. Students should recognize that they will need to:
Find out the measurements of the jewelry boxes and shipping boxes, as well as the costs for mailing a shipping box of each size. Asking students to find out this information themselves will increase the modeling demand (MP4).
Decide on an orientation for the jewelry boxes inside each shipping box and calculate how many jewelry boxes will fit with that particular orientation.
Test out different orientations and how they affect the number of jewelry boxes to be fitted and the cost.
Students may want to think of a strategy for considering different configurations efficiently, rather than testing all of them, which would be time consuming and repetitive. As students make plans to try out different jewelry box orientations and associated calculations, encourage them to work systematically to minimize omissions and errors. Urge students to create drawings or models of the boxes to show the calculations they will need to make.
Consider supporting students by discussing the different orientations of jewelry boxes in a shipping box (Which orientations are possible? How much empty space would result?) and possible ways to use drawings or diagrams to show the arrangements of jewelry boxes.
Launch
Give students 1–2 minutes to read the task statement individually and to ask any clarifying questions. Demonstrate the idea of the task by putting a small box inside a larger box in different orientations. Consider displaying USPS flat-rate boxes, or an image of each of the boxes.
Arrange students in groups of 4. Give students 5 minutes of quiet think time to brainstorm about what information is needed to solve this task and share to it with their group. Give another 5 minutes to plan in groups, followed by time to measure boxes or research box options and dimensions for themselves. Provide access to measuring tools.
USPS flat-rate information:
Small box:
\(5\frac38\)
inches by
\(8\frac58\)
inches by
\(1\frac58\)
inches. Cost:
$
6.80.
Medium box 1:
\(11\)
inches by
\(8\frac12\)
inches by
\( 5\frac12\)
inches. Cost:
$
13.45.
Medium box 2:
\(11\frac78\)
inches by
\(3\frac38\)
inches by
\( 13\frac58\)
inches. Cost:
$
13.45.
Large box:
\(12\)
inches by
\( 12 \)
inches by
\( 5\frac12\)
inches. Cost:
$
18.75.
Reading, Speaking, Representing: MLR6 Three Reads.
Use this routine to orient students to the context of the problem. In the first read, students read the problem with the goal of comprehending the situation (an artist is packing jewelry boxes to ship to a store.). Clarify any unknown language, such as a “flat-rate” box or shipping rates, as needed. For the second read, ask students to identify the quantities and mathematical relationships (number of necklaces ordered, the dimensions of the jewelry box). After the final read, ask students to brainstorm possible strategies they may use to solve the problem.
Design Principle(s): Support sense-making
Student Facing
An artist makes necklaces. She packs each necklace in a small jewelry box that is
\(1\frac34\)
inches by
\(2\frac14\)
inches by
\(\frac34\)
inch.
A department store ordered 270 necklaces. The artist plans to ship the necklaces to the department store using flat-rate shipping boxes from the post office.
Consider the problem: Which of the flat-rate boxes should she use to minimize her shipping cost?
What other information would you need to be able to solve the problem?
Discuss this information with your group. Make a plan for using this information to find the most inexpensive way to ship the jewelry boxes. Once you have agreed on a plan, write down the main steps.
Student Response
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Activity Synthesis
Reconvene as a class before continuing with the next part. Ask each group to share a couple of specific steps they have taken toward answering the question and a couple of steps they plan on taking to move forward. Highlight any ideas students might have about making the problem-solving process more efficient and systematic. If not already mentioned by students, suggest that each group divide up the calculations to be done so each person is responsible for one shipping box.


correct_option_index: 3