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: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
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: Optional activity
The purpose of this activity is for students to use equations to represent situations of percent increase and decrease. Additionally, students identify the original and new amount in the double number lines to reinforce what they learned in earlier lessons (that the original amount pertains to 100%).
As students work on the task, look for students who created various equations for the last question.
Launch
Show students the double number line from the activity in the previous lesson.
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Help them make connections to the first problem. Tell them that they can go back to the previous lesson to see the double number lines for the others if that helps.
Arrange students in groups of 2. Give 5–8 minutes of quiet work time. After 5 minutes allow students to work with a partner or to continue to work alone.
Representation: Internalize Comprehension.
Represent the same information through different modalities by using double number line diagrams. If students are unsure where to begin, suggest that they draw a double number line diagram to help organize the information provided.
Supports accessibility for: Conceptual processing; Visual-spatial processing
Student Facing
The gas tank in dad’s car holds 12 gallons. The gas tank in mom’s truck holds 50% more than that. How much gas does the truck’s tank hold? Explain why this situation can be represented by the equation
\((1.5) \boldcdot 12 = t\)
. Make sure that you explain what
\(t\)
represents.
Write an equation to represent each of the following situations.
A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold?
After a 25% discount, the price of a T-shirt was
$
12. What was the price before the discount?
Compared to last year, the population of Boom Town has increased by 25%.The population is now 6,600. What was the population last year?
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Anticipated Misconceptions
Students may continue to struggle to recognize the original amount and new amount with the proper percentages on the double number line. Remind them that the original amount always corresponds to 100%.
Activity Synthesis
Select students to share the values they identified as original amount and the new amount for a few problems. Discuss how 100% always corresponds to the original value and when there is an increase in the value the new value corresponds to a percentage greater than the original 100%.
Select students to share the different equations they came up with. Discuss how the distributive property is useful for finding the percentage that corresponds with the new value instead of the percentage of the change.
Discuss how solving problems about percent change may require either multiplying or dividing numbers. It can be confusing, but it helps to first express the relationship as an equation and then think about how you can find the unknown number. Looking at the examples below, the first two require multiplication, but the others require division.
Using the structure A% of B is C:
\((1.5) \boldcdot 12 = c\)
\((0.80) \boldcdot 15 = c\)
\(a \boldcdot (1,200) = 1,080\)
\(a \boldcdot (1.50) = 1.75\)
\((0.75) \boldcdot b = 12\)
\((1.25) \boldcdot b = 61, 600\)
Writing, Speaking: MLR1 Stronger and Clearer Each Time.
To begin the whole-class discussion, use this routine to give students a structured opportunity to revise and refine their response to the first question, "Explain why this situation can be represented by the equation
\((1.5) \boldcdot 12 = t\)
." Give students time to meet with 2–3 partners, to share and get feedback on their initial explanations. Provide listeners with prompts for feedback such as, “What does
t
represent?” “Where is 50% in the equation?” “Can you say that another way?” etc. Invite students to go back and refine their written explanation based on the peer feedback they receive. This will help students understand how situations of percent increase or decrease can be represented by an equation.
Design Principle(s): Optimize output (for generalization); Cultivate conversation


aligns: no