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

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fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Order three objects by length; compare the lengths of two objects indirectly by using a third object.
problem_activity: Narrative
The purpose of this activity is for students draw and shade rectangles with a unit fraction side length and a whole number side length. Then they find the areas of the shaded regions. The tactile experience of drawing and shading encourages students to count the number of shaded parts and then either reason about their size or think about moving them to make full unit squares. They also consider a diagram where not all of the unit squares are shown. Students estimate how many of the unit squares are hidden. This helps to highlight that finding the total area can be done with multiplication where one factor is the area of each shaded part and the other factor is the total number of shaded parts (MP7).
Required Materials
Materials to Copy
Grid Paper 5
Launch
Groups of 2
Give students grid paper.
Activity
5–7 minutes: independent work time
5 minutes: partner work time
Monitor for students who:
use the grid structure on the paper to draw their rectangles
count the number of unit squares that might be hidden under the yellow rectangle
Student Facing
Represent each rectangle on grid paper:
\(\frac{1}{2}\)
unit by 1 unit
\(\frac{1}{2}\)
unit by 2 units
\(\frac{1}{2}\)
unit by 3 units
\(\frac{1}{2}\)
unit by 4 units
Find the area of each rectangle that you drew.
What information do you need to find the area of the shaded region?
[IMG]
What might the area of the shaded region be? Explain or show your reasoning.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
If students do not draw the rectangles correctly, show them the shaded region from the previous activity with side lengths 6 units and
\(\frac{1}{2}\)
unit and ask “How could you adapt this diagram to show a rectangle that is 4 units by
\(\frac{1}{2}\)
unit?”
Activity Synthesis
Display a student generated image of the
\(\frac{1}{2}\)
unit by 4 unit rectangle.
Ask previously selected students to describe how they drew they 4 by
\(\frac{1}{2}\)
rectangle.
Display image from student workbook of the rectangle that is partly covered.
“What do you need to know to determine the area of the shaded region?” (We need to know how many unit squares are under the yellow rectangle.)
“How many unit squares do you think make up the rectangle?” (6 or 7)
“How did you use the number of these unit squares to make an estimate for the shaded region?” (I know that each shaded blue rectangle is
\(\frac{1}{2}\)
of a square so if there are 6 or 7 of those, that would be
\(\frac{6}{2}\)
or
\(\frac{7}{2}\)
square units.)


aligns: no