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

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
In this activity, students compare pairs of numbers with the same number of digits and the same set of digits (for example, 278 and 872, or 1,356 and 3,156). The goal is to elicit the idea that both the placement and the size of the digits matter in determining the value of a number, and that the digits in certain places matter more than others for making comparisons (MP7).
Required Materials
Materials to Gather
Number cards 0–10
Launch
Groups of 3–4
Give each group a set of cards 0–10. Ask students to remove the cards that show 10.
“What three-digit numbers can we make with 5, 7, and 3?” (357, 375, 537, 573, 735, 753)
Activity
“Work with your group to make pairs of numbers using the digits on the cards. First use 3 cards, then 4, then 5, and lastly 6. Compare each pair of numbers.”
“Think about how you go about comparing each pair of numbers.”
5 minutes: group work time
Monitor for students who:
notice that not all digits need to be compared in order to tell which number in a pair is greater
use place-value language in describing the numbers
make two numbers with the same first digit or the same first and second digits
Student Facing
Your teacher will give you a set of cards, each with a single digit, 0–9.
[IMG]
Use the cards for 2, 7, and 8 to make two different three-digit numbers. Use < or > to compare them.
\(\boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \underline{\hspace{0.5in}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}}\)
Now include the digit 1 to make two different four-digit numbers. Compare the numbers.
\(\boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \underline{\hspace{0.5in}} \ \boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}}\)
Shuffle the cards. Repeat what you did earlier with new cards.
Four-digit numbers
\(\boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \underline{\hspace{0.5in}} \ \boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}}\)
Five-digit numbers
\(\boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \underline{\hspace{0.5in}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}}\ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \)
Six-digit numbers
\(\boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \underline{\hspace{0.5in}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} _{\ \huge{,}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \ \boxed{\phantom{\frac{00}{00}}} \)
For each pair you compared, how did you decide which number is greater?
Student Response
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Advancing Student Thinking
When answering the question about how they compared the numbers, students may say that they “just know” which one was greater. Encourage them to think about the features of the numbers that gave them an immediate clue about the size of the numbers, or the features that they didn’t find as useful.
Activity Synthesis
Select students to display their number statements and read them. Ask if the class agrees with their comparison.
“How did you decide which number is greater? Did you compare every digit?”
Select students who wrote numbers with the same first digit (or the same first two digits) to share their number statements. Ask them to explain how they compared the numbers.
If no students mentioned that the digits in some places matter more than those in others, ask them about it.
“Did you pay attention only to some digits but not others?”
“Which ones did you prioritize? Were there any you tended to ignore?”


aligns: yes