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: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
problem_activity: Activity
In this activity, students see that withdrawals, in addition to debts, can also be represented using negative numbers. Students continue using addition and subtraction to solve problems about debt. While solving the last problem, students may begin wondering about multiplying and dividing signed numbers, which will be addressed in the next several lessons.
You may wish to ask students to pause after the first question for discussion. The decision about which numbers to represent with positive versus negative values hinges on whether you are thinking from the perspective of the person or the perspective of the account. Point out that the final balance is represented with a negative number to show that the person owes the bank money (this should be brought out in the launch). Therefore, from the perspective of the account, deposits are positive values and withdrawals are negative values. It would be possible to proceed either way, but it will facilitate discussion later if everyone uses the same convention as a result of work on the first question.
As students work, monitor for students who are expressing their reasoning as addition and subtraction equations or expressions.
Launch
Display the bank statement image for all to see, without the questions. Ask students to think of two things they notice and two things they wonder. Give students 1 minute of quiet think time. Select a few students to share. Make sure students understand the meaning of
deposit
and
withdrawal
.
Give students quiet work time followed by whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Reading, Writing: MLR5 Co-craft Questions.
To support students in making sense of the bank statement, display the image of the bank statement without the remaining text of the problem. Clarify the meaning of the terms in the bank statement (e.g., deposit, withdrawal, balance) in this context. Note that the word “balance” has an everyday meaning (“I fell down when I lost my balance”). Then ask pairs of students to write down possible mathematical questions that might be asked about the situation. Invite pairs to share with the whole class. Highlight questions that relate to calculating a balance based on a given deposit or withdrawal. This will allow students to use mathematical language related to a bank statement as they reason about the accounting situation.
Design Principle(s): Cultivate conversation; Support sense-making
Student Facing
Here is a bank statement.
[IMG]
If we put withdrawals and deposits in the same column, how can they be represented?
Andre withdraws
$
40 to buy a music player. What is his new balance?
If Andre deposits
$
100 in this account, will he still be in debt? How do you know?
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
The
national debt
of a country is the total amount of money the government of that country owes. Imagine everyone in the United States was asked to help pay off the national debt. How much would each person have to pay?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
The most important thing for students to understand is that the rules for adding and subtracting signed numbers can help them solve problems about debts.
Select students to share their solutions. Ask students to indicate whether they agree, disagree, or have any clarifying questions.


aligns: no