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: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
problem_activity: Task
Arianna has been saving her chore money all summer. Her mother has allowed her to
spend the money on school supplies of Arianna’s choosing. Here are some of her favorite
items and the price for each:
[IMG]
{"table": [{"tbody": [{"tr": [{"td": [{"_value": "Lunchbox"}, {"_value": "Art Supplies"}, {"_value": "Pencil Box"}, {"_value": "Mechanical Pencil"}]}, {"td": [{"_value": "\\$2 and 50\u00a2"}, {"_value": "75\u00a2"}, {"_value": "$1 and 25\u00a2"}, {"_value": "45\u00a2"}]}]}]}]}
Arianna has four dollars and twenty-five cents to spend.
Select two items she might choose to purchase. What is the total cost of these two items?
Select three items she might choose to purchase. What is the total cost of these three items? How much money will Arianna have left over if she buys these three items
How many pencil boxes can Arianna buy without going over the $4 and 25¢ she has saved?
Explain your thinking for part (c) in words.


aligns: no