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 problem or activity shown below 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: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)
problem_activity: Problem 1
Represent each fraction as a percent by completing the table. Use the two double number lines below to show your work.
{"table": [{"_attributes": {"class": ["table", "table-bordered", "table-condensed"], "style": "width: 90%;"}, "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "Fraction"}], "td": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{10}$$"}]}, {"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{4}$$"}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{2}{10}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{5}$$"}], "_value": "or"}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{1}{2}$$"}]}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{3}{4}$$"}]}]}, {"p": [{"_attributes": {"style": "text-align: center;"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{8}{10}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$\\frac{4}{5}$$"}], "_value": "or"}]}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "Percent"}], "td": [{}, {}, {}, {}, {}, {}]}]}]}]}
[IMG]
Problem 2
Answer the questions below using mental math. Use your double number lines from Anchor Problem 1 if you need to.
a.   What is
$$\frac{1}{2}$$
of 20?
b.   What is 50% of 20?
c.   What is 10% of 60?
d.   What is 20% of 60?
e.   What is
$$\frac{1}{4}$$
of 48?
f.   What is 25% of 48?
g.   What is 75% of 48?
h.   What is 10% of 125?
i.   A textbook that costs $36 is on sale for 25% off. How much money will you save?
Problem 3
Answer the questions below using mental math. Use your double number lines from Anchor Problem 1 if you need to.
a.   5 is 50% of what number?
b.   12 is 10% of what number?
c.   15 is 25% of what number?
d.   30 is 75% of what number?
e.   400 is 20% of what number?
f.   A coat is on sale for 10% off. You save $18. What was the original price of the coat?
Problem 4
Answer the questions below using mental math. Use your double number lines from Anchor Problem 1 if you need to.
a.   24 is what percent of 240?
b.   350 is what percent of 700?
c.   20 is what percent of 80?
d.   30 is what percent of 40?
e.   80 is what percent of 80?
f.   You saved $4 on a book that originally cost $16. What percent of the original cost did you save?


aligns: no