few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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?

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fl_problem_001097_neg_0

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standard_description: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)
problem_activity: Activity
In this activity, students are given a percent increase and use it to calculate the new value, rather than being given the original and new values to calculate the percent increase. Students can solve the problems using the double number lines but the discussion that follows will be the connection to what the words specifically mean (MP6).
As students work, monitor for students who complete the double number line diagram and any student that uses other methods to correctly reason about the problem.
Launch
Arrange students in groups of 2. Give students 5 minutes of quiet work time followed by partner then whole-class discussion.
Student Facing
​​
A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much cereal does the box come with now?
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​​
The price of a shirt is \$18.50, but you have a coupon that lowers the price by 20%. What is the price of the shirt after using the coupon?
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Student Response
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Anticipated Misconceptions
Have students use the double number line diagram if they need help figuring out 20% more.
Activity Synthesis
Select students to share their reasoning for each problem. Start with a student that used the double number line diagram to solve the problem. Then, have students share other methods they used to solve the problem, such as multiplying by 1.2 and 0.8.
Ask students:
Did the number of ounces of cereal in the cereal box increase or decrease?
What percentage of the original amount of cereal is the new amount of cereal?
Did the price of the shirt increase or decrease?
What percentage of the original price of the shirt is the new price of the shirt?
Tell students that the change on the cereal box is an example of a
percent increase
. The discount on the shirt is an example of a
percent decrease
. You might want to mention that in both cases, 100% always corresponds to the original amount before the change; however, future activities will address this concept in depth.
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of percent increase and percent decrease.
Supports accessibility for: Conceptual processing; Language
Writing: MLR3 Clarify, Critique, Correct.
Before students share their reasoning for each problem, present an incomplete strategy for finding the discount price for the shirt. For example, “The discount is 20%, so the price of the shirt is $3.70.” Ask students to critique the reasoning, and work with a partner to write an improved explanation. Listen for and amplify the language students use to make sense of what is displayed (e.g., “I think they ___ because ____.”), as well as the mathematical language that students use that strengthen their explanations. This will support student understanding of mathematical language related percent increase and percent decrease.
Design Principle(s): Maximize meta-awareness


aligns: no