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: 
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_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Add up to four two-digit numbers using strategies based on place value and properties of operations.
problem_activity: Narrative
The purpose of this activity is for students to use their understanding of place value to determine the number described in a riddle. Students then write the number of hundreds, tens, and ones, and represent the value as a three-digit number.
MLR8 Discussion Supports.
Display sentence frames to support partner discussion about each number written on the table: “I agree because . . .” or “I disagree because . . . .”
Advances: Conversing
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide the order in which they complete the work. They can start with any of the riddles, as long as they complete all of them.
Supports accessibility for: Attention, Social-Emotional Functioning
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
“I have 4 hundreds, 3 ones, and 2 tens.”
“Which of these shows the total value written as a three-digit number? Explain how you know.”
Display 432, 234, 423.
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
“You are going to solve number riddles using base-ten blocks.”
As needed, demonstrate the task with a student.
“Take turns reading the clues, while your partner uses blocks to make the number.”
“Make sure you agree before adding each number to the table.”
10 minutes: partner work time
If students finish early, ask them to write their own riddles and trade them with other groups to solve.
Monitor for students who recognize they need a zero when writing the three-digit number in places where there were no tens or no ones.
Student Facing
Solve each riddle and write the three-digit number. Use the table to help you organize the digits.
| riddle | hundreds | tens | ones | three-digit number |
|--------|----------|------|------|--------------------|
|   1    |          |      |      |                    |
|   2    |          |      |      |                    |
|   3    |          |      |      |                    |
|   4    |          |      |      |                    |
|   5    |          |      |      |                    |
|   6    |          |      |      |                    |
I have 2 ones, 7 tens, and 6 hundreds.
I have 3 ones, 5 tens, and 2 hundreds.
I have 7 hundreds, 5 ones, and 3 tens.
I have 5 hundreds, no tens, and 9 ones.
I have 4 ones, 6 tens, and 3 hundreds.
I have 8 tens, 1 hundred, and no ones.
Student Response
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Activity Synthesis
Invite previously selected students to share what they noticed when writing 509 and 180.
As needed, write 81, 801, and 810 and ask, “What is the difference between 81, 801, and 810?”


aligns: no