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.


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.

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

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
problem_activity: Activity
In this activity, students practice reasoning about the amount in one group in division situations. They continue to write equations and draw diagrams to support their reasoning. In two problems (odd-numbered), the given number of groups is greater than 1. In the other two problems (even-numbered), a fraction of a group is given. Though this does not affect the structure of the equations students write, students need to take care to reflect this information correctly in their diagrams.
Students choose two problems to solve and work in groups of 2. Time permitting, students create a visual display of their work and conclude the activity with a gallery walk.
Launch
Arrange students in groups of 2. Ask each group to choose two problems: an even-numbered problem and an odd-numbered problem. Give students 7–8 minutes of quiet time to work on their two chosen problems, and a few minutes to share their work with their partner.
Provide access to geometry toolkits and tools for creating a visual display. If time permits, ask each group to create a visual display of their solution and reasoning for one problem. Emphasize that they should organize their reasoning so it can be followed by others.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Provide students with access to blank tape diagrams to support information processing.
Supports accessibility for: Visual-spatial processing; Organization
Student Facing
Write a multiplication equation and a division equation and draw a diagram to represent each situation. Then, find the answer and explain your reasoning.
Jada bought
\(3\frac12\)
yards of fabric for
$
21. How much did each yard cost?
\(\frac 49\)
kilogram of baking soda costs
$
2. How much does 1 kilogram of baking soda cost?
Diego can fill
\(1\frac15\)
bottles with 3 liters of water. How many liters of water fill 1 bottle?
\(\frac54\)
gallons of water fill
\(\frac56\)
of a bucket. How many gallons of water fill the entire bucket?
Student Response
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Student Facing
Are you ready for more?
The largest sandwich ever made weighed 5,440 pounds. If everyone on Earth shares the sandwich equally, how much would you get? What fraction of a regular sandwich does this represent?
Student Response
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for free access to Extension Student Response.
Activity Synthesis
Arrange for groups that are assigned the same problem to present their visual displays near one another. Give students a few minutes to visit the displays and to see how others reasoned about the same two problems they chose. Before students begin a gallery walk, ask them to be prepared to share a couple of observations about how their strategies and diagrams are the same as or different from others’.
After the gallery walk, invite a couple of students to share their observations. Tell them that, in upcoming lessons, they will investigate other ways to reason efficiently about division problems.
Speaking, Representing: MLR8 Discussion Supports.
Give students additional time to make sure that everyone in their group can explain the equations and diagrams they created. Prompt groups to rehearse what they will say when they share with another group. Rehearsing provides students with additional opportunities to speak and clarify their thinking. This will also help students improve the quality of their explanations during the whole-class discussion.
Design Principle(s): Optimize output (for explanation)


aligns: no