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: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
problem_activity: Narrative
The purpose of this activity is for students to use what they know about counting within 1,000 to make sense of number lines that show counting on or counting back by 10 or 100. This work helps build fluency with counting within 1,000 and connects to an upcoming lesson where students add and subtract multiples of 10 or 100 using equations.
MLR8 Discussion Supports.
Invite students to begin partner interactions by repeating the question, “What pattern do you notice?” This gives both students an opportunity to produce language.
Advances: Conversing
Launch
Groups of 2
Display the number line with jumps of 100.
“On this number line there are 5 tick marks, but only 3 are labeled. What are the missing numbers and how do you know?” (534 and 634 because the jumps are the same length and they must be jumps of 100. The hundreds place is increasing by 1, but the other places are not changing.)
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
“You recognized that the length between each tick mark must represent 100. The tick marks and arrows show counting on by 100 on the number line.”
Activity
“For each of the problems, use what you know about counting, representing numbers on the number line, and place value to find the missing numbers.”
10 minutes: partner work time
Monitor for a student to share their reasoning for _____, _____, 332, 342, 352
Student Facing
[IMG]
Fill in the missing numbers.
[IMG]
Does this number line show counting on by 10 or counting on by 100?
Fill in the missing numbers.
[IMG]
Does this number line show counting on by 10 or counting on by 100?
Fill in the missing numbers.
[IMG]
Does this number line show counting on by 10 or counting on by 100?
Fill in the missing numbers to show counting on by 10.
739, 749, __________, 769, __________
Explain how you can tell your numbers show counting on by 10 and not counting on by 100.
Student Response
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Advancing Student Thinking
If students find the missing numbers by counting by 1 instead of using patterns increasing by 10 or 100, consider asking:
“What digit is changing? Is it going up or down?”
“How can that help you figure out the count?”
Activity Synthesis
Invite a student to share their reasoning for _____, _____, 332, 342, 352.
“How did you figure out the starting number?” (I saw that it was going up by 10, so I knew I had to count back by 10 to find the starting numbers.)
Record responses with an open number line and equations.


aligns: no