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: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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

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fl_problem_001097_neg_0

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fl_problem_001894_neg_0

HS_0
standard_description: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
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
click here to register or sign in
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