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: Compare two numbers between 1 and 10 presented as written numerals.
problem_activity: Narrative
The purpose of this activity is for students to compare numbers in a way that makes sense to them. Students can use physical objects or make drawings to represent each number (MP5), and match or count to compare. Students can also use their knowledge of the count sequence and understanding that each successive number refers to a quantity that is one more to compare the numbers. In the synthesis students describe how creating representations of numbers helps to compare numbers.
Action and Expression: Internalize Executive Functions.
After students decide which manipulative they will use for the activity, invite students to plan a strategy for how they will use their manipulatives to determine which number is more. If students choose to use counters, give them access to 5-frames to help with the counting.
Supports accessibility for: Visual-Spatial Processing, Conceptual Processing, Organization
Required Materials
Materials to Gather
Connecting cubes or counters
Launch
Groups of 2
Give students access to connecting cubes or counters.
“Work with your partner to figure out which number is more. Circle the number that is more.”
Activity
5 minutes: partner work time
Monitor for students who create representations of the numbers using cubes or a drawing and use these representations to compare.
Monitor for students who counted to figure out which number is more.
Student Facing
Circle the number that is more.
[IMG]
[IMG]
[IMG]
[IMG]
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 circle the number that is less instead of the number that is more, consider asking:
“What do you know about these two numbers? What are you trying to figure out?“
“How can you use the cubes to show each number? How can the cubes help you figure out which number is more?“
Activity Synthesis
Invite previously selected students to share the representations they made and how they used them to figure out which number is more.
“How did counting out the groups of objects or drawing pictures help you figure out which number is more?”
Invite previously selected students to share how counting helped them compare the numbers.
“We know 8 is more than 5. Compare these numbers using ‘less’.”


aligns: yes