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: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Problem 1
Look at the title and image of the Newsweek article,
More Than Half of Medical Advice on 'Dr. Oz' Lacks Proof or Contradicts Best Available Science: Study
.
According to this article, a research team looked at 80 pieces of medical advice from
The Dr. Oz Show
and found no evidence to support 43 of these recommendations.
a.   Do you agree or disagree with the claim in the headline based on this information? Why or why not?
b.   Determine whether the following fractions are greater or less than
$$\frac12$$
.
$$\frac{5}{12}$$
$$\frac35$$
Problem 2
a.   Ishmael says that he knows
$$\frac{5}{12}$$
is less than
$$\frac35$$
because
$$\frac{5}{12}$$
is less than
$$\frac12 $$
and
$$\frac35$$
is more than
$$\frac12$$
, so
$$\frac{5}{12}$$
must be less than
$$\frac35$$
. Explain why Ishmael’s reasoning is correct using words or pictures.
b.   Use Ishmael’s strategy to compare the following pairs of fractions. Record your answer with
$$\lt$$
,
$$\gt$$
, or
$$=$$
.
$${{4\over10}}$$
and
$${{5\over8}}$$
$${{7\over12}}$$
and
$${{4\over9}}$$
$${{1\over3}}$$
and
$${{4\over7}}$$
Problem 3
a.   Now Joslyn is comparing
$$\frac46$$
and
$$\frac58$$
. She says that she knows
$$\frac46$$
is more than
$$\frac58$$
because
$$\frac46$$
is
$$\frac16$$
more than
$$\frac12$$
and
$$\frac58$$
is
$$\frac18$$
more than
$$\frac12$$
and
$$\frac16$$
is more than
$$\frac18$$
. Explain why Jocelyn’s reasoning is correct using words or pictures.
b.   Use any strategy to compare the following pairs of fractions. Record your answer with
$$\lt$$
,
$$\gt$$
, or
$$=$$
.
$$\frac{5}{12}$$
and
$${{4\over10}}$$
$${{3\over5}}$$
and
$${{5\over9}}$$
$${{1\over3}}$$
and
$${{3\over7}}$$


aligns: yes