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 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_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
problem_activity: Narrative
In this activity, students are given expressions that represent strategies for finding the area of rectangles. The strategies are based on the distributive property and the associative property of multiplication. Students interpret the expressions by marking or shading area diagrams and connect each expression to the product of two factors (MP2). For instance, they see that to find the value of
\(2 \times (2 \times 6)\)
is to find the value of
\(4 \times 6\)
or
\(6 \times 4\)
.
MLR8 Discussion Supports:
Synthesis: Create a visual display of the diagrams. As students share their strategies, annotate the display to illustrate connections. For example, trace the area showing 5 columns of 3, and write
\(5 \times 3\)
.
Advances: Speaking, Representing
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 2 of the 3 problems to complete.
Supports accessibility for: Organization, Attention, Social-emotional skills
Required Materials
Materials to Gather
Colored pencils, crayons, or markers
Launch
Groups of 2
“Take a minute to read the directions of the activity. Then, talk to your partner about what you are asked to do.”
1 minute: quiet think time
1 minute: partner discussion
Answer any clarifying questions from students.
Give students access to colored pencils, crayons, or markers.
Activity
“Mark or shade each diagram to represent how each student found the area.”
3–5 minutes: independent work time
“Share with your partner how you used the rectangles to show each expression.”
3–5 minutes: partner discussion
Student Facing
Here are some rectangles and expressions that show how three students saw the area of the rectangles.
Noah
[IMG]
\((5\times 3)+(2 \times 3)\)
Priya
[IMG]
\(2 \times (2 \times 6)\)
Tyler
[IMG]
\((5 \times 8) + (3 \times 8)\)
For each rectangle:
Name the two factors that can be multiplied to find its area.
Mark or shade each rectangle to show how each student saw the area. Be prepared to explain your reasoning.
Student Response
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Activity Synthesis
“What are the two factors you can multiply to find the area of Noah’s rectangle?” (7 and 3)
“How are those numbers related to the expression that he wrote:
\((5\times 3)+(2 \times 3)\)
?”  (
\(7 \times 3\)
is 21. Finding
\(5\times3\)
, which is 15, then adding
\(2\times3\)
, which is 6, also gives 21.)
“Where do you see the two factors in his expression?” (The 7 is 5 and 2 combined. The 3 is in the
\(5 \times 3\)
and
\(2 \times 3\)
.)
Repeat the line of questioning with Priya’s rectangle and expression.


aligns: yes