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?

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to represent addition and subtraction equations on a number line. Students consider where to begin and in which direction to draw their arrows in order to accurately represent the operation in the given equation. Throughout the activity, encourage students to explain how they know their representation matches the equation. Listen for the way they explain how they know where to start and end their arrow, which direction they draw their arrow, and how they connect the length the jump represents to the equation (MP3).
MLR8 Discussion Supports.
Display sentence frames to support partner discussion: “Our number lines are the same because…”. “Our number lines are different because…”.
Advances:Speaking, Conversing
Launch
Groups of 2
“We have seen addition and subtraction equations represented on a number line. How can you tell whether a number line is representing addition or subtraction?” (Look at the direction of the arrow.)
30 seconds: quiet think time
Share responses.
Activity
“Now you are going to represent some equations on number lines. Be sure others will be able to tell from looking at your number line whether you are representing addition or subtraction.”
8 minutes: independent work time
Monitor for students who:
Mark the first number and last number in each equation with a point first. Then draw their arrow to match the operation.
Locate the first number in the equation, count a number of spaces forward or backward to match the operation, and draw an arrow to connect the two numbers.
“Compare your number lines with your partner. Explain how you know your representation matches the equation.”
3 minutes: partner discussion
Student Facing
Represent each equation on the number line.
\(15 + 7 = 22\)
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\(18 - 6 = 12\)
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\(46 + 7 = 53\)
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\(33 - 9 = 24\)
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Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If a student's number line representation doesn't match the equation, consider asking:
“Will you please explain your representation?”
“How did you decide where to start or end on the number line?”
“How did you decide which direction to draw your arrow?”
Activity Synthesis
Display the equation and blank number line for
\(15 + 7 = 22\)
.
Invite previously selected students to share how they represented the equation on the number line.
Consider asking:
“How do you see each number in the equation in ____’s representation?”
“How do you know ___’s representation matches the operation (addition or subtraction)?”
As time permits, continue with the other equations.


aligns: no