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

shot_info: im_task_001477_neg_0

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fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this activity is to represent and solve a measurement problem with fractions. Students may approach this activity in multiple ways and are invited to apply what they know about operations with fractions, comparing fractions, and fraction equivalence to make sense of and solve the problems (MP2). Throughout the activity, listen for the ways students use what they know about comparing fractions and fraction equivalence as they make sense of the problem. Although students may consider ways to subtract fractions with unlike denominators, this is not a requirement for grade 4. Focus the conversation during the activity and the synthesis on how students can solve the problem by reasoning about equivalent fractions and the representation they use to make sense of the problem.
MLR8 Discussion Supports.
Synthesis: Create a visual display of the diagrams. As students share their strategies, annotate the display to illustrate connections. For example, next to each representation, write how the diagram relates to the situation.
Advances: Speaking, Representing
Launch
Groups of 2
Activity
5 minutes: independent work time
5 minutes: partner work
Monitor for different representations of the situation (for example, equations, drawings, and number lines).
Student Facing
In science class, Noah, Tyler, and Jada are building a model of a roller coaster out of 1-foot-long paper straws.
Noah needs a piece that is
\(\frac{7}{12}\)
foot long.
Tyler needs one that is
\(\frac{1}{4}\)
foot long.
Jada needs one that is shorter than the other two.
Jada says, “We can just use one straw for all these pieces.”
[IMG]
Draw a diagram to represent this situation and explain to your partner how it matches the situation. Then, find the length of the piece of straw that could be Jada’s piece.
Did Noah use more than
\(\frac{1}{2}\)
foot or less than
\(\frac{1}{2}\)
foot of straw? Explain or show your reasoning.
Tyler says, “If Jada uses a piece that is
\(\frac{1}{6}\)
foot long, there would be a piece of straw that is
\(\frac{1}{12}\)
foot left.”
Do you agree or disagree with Tyler? Explain your reasoning.
Student Response
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Advancing Student Thinking
If students create representations that do not match the quantities in the problem, consider asking:
“How does your representation show the length of the straw? How does it show Noah and Tyler’s pieces?”
“How does your representation show the action in the situation?”
Activity Synthesis
Invite previously selected students to share their arguments and allow peers to extend and add ideas to the conversation.
“How does each representation match this situation about the straw?” (They each show the total length of the straw and ways it could be broken into smaller parts. They each show the length of Noah and Tyler’s pieces. They show how long Jada’s piece could be.)


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