few_shots: 
Example 1:
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.

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.


Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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
$$-\frac{1}{4}$$


Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
problem_activity: Narrative
The purpose of this activity is for students to convert from meters to centimeters using the context of a standing broad jump, a common test for physical fitness. Students may multiply by 100 to convert from meters to centimeters or divide by 100 to convert from centimeters to meters. Students should be encouraged to use whatever strategy makes sense to them. Future lessons will focus specifically on conversion from centimeters to meters. Give students access to meter sticks.
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Required Materials
Materials to Gather
Metersticks
Launch
Groups of 2
Display the image from student workbook.
Give students access to meter sticks.
“What do you notice? What do you wonder?” (The girl is jumping. There are numbers on the mat. Did she start where the footprints are? How far did she jump?)
Activity
1–2 minutes: quiet think time
6–8 minutes: partner work time
Monitor for students who:
use their result for Tyler’s jump in centimeters to find his jump in millimeters
use the result in meters to find how far Tyler jumped in millimeters
Student Facing
[IMG]
[IMG]
Here are the distances that each student jumped.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "student"}, {"_attributes": {"scope": "col"}, "_value": "distance"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "Mai"}, {"_value": "1.61 meters"}]}, {"td": [{"_value": "Tyler"}, {"_value": "1.43 meters"}]}, {"td": [{"_value": "Clare"}, {"_value": "1.57 meters"}]}]}]}]}
The average standing broad jump distance for 5th graders is 148 centimeters. Are each of the students in the table below, at, or above the average? Explain or show your reasoning.
The world record for the standing broad jump is 337 centimeters. Jada says that’s more than Mai and Clare jumped combined. Do you agree with Jada? Explain or show your reasoning.
Tyler says his jump sounds more impressive if he reports it in millimeters.
How far is Tyler’s jump in millimeters? What about Mai’s and Clare’s jumps?
Which unit do you think is best for reporting the jumps? Explain your reasoning.
Student Response
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Advancing Student Thinking
If students do not know the relationship between millimeters, centimeters, and meters, show them a meter stick and ask “How can you use the meter stick to figure out how many millimeters are in 1 meter?”
Activity Synthesis
Display the expression:
\(1.43 \times 100\)
.
“How does this expression represent Tyler’s jump in centimeters?” (There are 100 centimeters in a meter.)
Invite students to share how they found Tyler’s jump in millimeters.
Display the expression:
\((1.43 \times 100) \times 10\)
.
“In what unit of measurement does this expression represent Tyler's jump? How do you know?” (It represents Tyler’s jump in millimeters. There are 10 millimeters in a centimeter and
\(1.43\times100\)
represents the centimeters, so if we multiply the number of centimeters by 10, we will get the number of millimeters.)
Display the expression:
\(1.43 \times 1,\!000\)
.
“How does this expression represent Tyler’s jump in millimeters?” (There are 1,000 millimeters in a meter so I have to multiply by 1,000 to get millimeters from meters.)
Display the equation:
\(1.43 \times 1,\!000 = (1.43 \times 100) \times 10\)
.
Invite students to share which unit they prefer to express the distances that the students jumped.
“It’s important to choose a unit that makes sense to you.”


aligns: no