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 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_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)
problem_activity: Narrative
The purpose of this activity is for students to draw two diagrams that represent a unit fraction of a unit fraction. Students work with the same unit fractions in both diagrams. The directions were intentionally written to encourage students to partition a unit square in different ways. Students initially partition the square into thirds in the first problem and into fourths in the second problem. Students may complete the diagrams in a way that makes sense to them. During the synthesis, students will connect both of the diagrams to the expressions
\(\frac {1}{4} \times \frac {1}{3}\)
and
\(\frac {1}{3} \times \frac {1}{4}\)
.
Launch
Groups of 2
Activity
2 minutes: Independent work time
10 minutes: partner work time
Monitor for students who:
draw diagrams like those in the student responses
recognize that both diagrams have the same amount shaded
can explain the different ways they partitioned each diagram
Student Facing
Show
\(\frac{1}{3}\)
of the square.
Shade
\(\frac{1}{4}\)
of
\(\frac{1}{3}\)
of the square.
How much of the whole square is shaded?
[IMG]
Show
\(\frac{1}{4}\)
of the square.
Shade
\(\frac{1}{3}\)
of
\(\frac{1}{4}\)
of the square.
How much of the whole square is shaded?
[IMG]
How are the diagrams the same and how are they different?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not identify how much of the whole square is shaded, ask: “How can you adapt your diagram to show how many pieces would be in the whole square?”
Activity Synthesis
Ask previously selected students to share their responses in the order given.
“How are the diagrams the same?” (They both have
\(\frac {1}{4}\)
and
\(\frac {1}{3}\)
in them. They both have
\(\frac {1}{12}\)
of the whole square shaded.)
“How are the diagrams different?” (In one diagram, I started by showing
\(\frac {1}{3}\)
of the square and then shaded in
\(\frac {1}{4}\)
of
\(\frac {1}{3}\)
. In the other diagram, I started by showing
\(\frac {1}{4}\)
of the square and then shaded in
\(\frac {1}{3}\)
of
\(\frac {1}{4}\)
.)
Display:
\(\frac{1}{12}\)
,
\(\frac{1}{4}\times\frac{1}{3}\)
,
\(\frac{1}{3}\times\frac{1}{4}\)
“How do the diagrams represent these expressions?”
Adapt diagrams as needed in order to show all three expressions.
“How do we know that both squares have the same amount shaded?” (They both have
\(\frac {1}{12}\)
shaded.)


aligns: no