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 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

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
problem_activity: Narrative
The purpose of this activity is for students to find the value of differences within 10. Students are encouraged to think about how patterns in subtraction problems and knowing sums within 10 can help them find the value of the differences. Students may use take away or counting on methods. The problems are written for students to think about different methods for solving. For example, students may find the value of
\(10 - 3\)
by taking away 3 to get 7, then see that they can find
\(10 - 7\)
by knowing the relationship between 3, 7, and 10. Students should work in groups of 2, with a different partner than they had in the previous activity.
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide which problem to start with.
Supports accessibility for: Social-Emotional Functioning, Attention
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to connecting cubes or two-color counters.
Activity
Read the task statement.
“You will first find the value of each difference on your own. Then you will share your thinking with a different partner than last activity.”
5 minutes: independent work time
2 minutes: partner discussion
Student Facing
Find the value of each difference.
\(9 - 6\)
\(10 - 3\)
\(7 - 3\)
\(9 - 5\)
\(8 - 6\)
\(6 - 5\)
\(9 - 4\)
\(10 - 7\)
Student Response
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Activity Synthesis
“Were there any expressions that helped you with another expression? How did they help you?” (
\(10 - 3\)
and
\(10 - 7\)
. They are related because
\(3 + 7 = 10\)
.
\(9 - 6\)
,
\(9 - 5\)
, and
\(9 - 4\)
. There is a pattern. Since the number being subtracted gets 1 bigger, the difference gets 1 smaller.)


aligns: no