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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
problem_activity: Problem 1
Josie makes 1.7 liters of lemonade. Josie’s mom tells her to split it evenly with her brother. How much lemonade, in liters, will Josie and her brother each get?
Problem 2
Here is how Mai used base-ten diagrams to calculate 0.62 ÷ 5. She started by representing 0.62.
[IMG]
She then made 5 groups, each with 1 tenth. There was 1 tenth left. She unbundled it into 10 hundredths and distributed the hundredths into 5 groups. Here is her diagram for 0.62 ÷ 5.
[IMG]
Mai should have a total of 12 hundredths, but her diagram shows only 10. Why?
She did not originally have thousandths, but in her diagrams each group has 4 thousandths. Why?
What value has Mai found for 0.62 ÷ 5?
Problem 3
Here is how Lin calculated 0.62 ÷ 5.
|                 Lin wrote the dividend, 0.62, and the divisor, 5.                  | She subtracted 5 groups of different amounts from 0.62, starting with 5 groups of 0.10, then 5 groups of 0.02. |                Lin wrote 0 to the right of the 2, which made 0.020.                | Lastly, she subtracted 5 times 0.004 from 0.020, which left no remainder.                          Then she added 0.100 + 0.020 + 0.004, which gave a quotient of 0.124. |
|------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/9FyZXfKqijxVpRgv2Bc6qf_CDWBZL.png |               .. image:: https://d21royfkw9g4l6.cloudfront.net/nxKMGc5DKRKgY6x2FVmo07_YDGM41.png               | .. image:: https://d21royfkw9g4l6.cloudfront.net/O3iHOw3zlpAkiFdwXHFNPB_NVXARD.png |                                            .. image:: https://d21royfkw9g4l6.cloudfront.net/91UkRicG3K9xdXGPqEsgOT_06NZSH.png                                            |
Lin put a 0 after the remainder of 0.02. Why? Why does this 0 not change the value of the quotient?
What value did Lin find for 0.62 ÷ 5?
Problem 4
Solve. Show or explain your work.
27 ÷ 6
0.84 ÷ 8
18.03 ÷ 6
3 ÷ 4


aligns: yes