few_shots: 
Example 1:
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.

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.


Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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
$$-\frac{1}{4}$$


Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is for students to practice using the subtraction algorithm introduced in a previous lesson. Provide base-ten blocks for students who choose to use them to support their reasoning about the algorithm.
MLR8 Discussion Supports:
Synthesis: Before students share their reasoning, remind them to use words such as decompose, ones, tens, and hundreds.
Advances: Speaking, Representing
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 3 of 5 problems to complete.
Supports accessibility for: Organization, Attention, Social-emotional skills
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Display Kiran’s algorithm from the previous lesson.
“Here’s a subtraction algorithm you saw in an earlier lesson. What might be the first thing you’d do if you are to use this algorithm to find the value of the subtraction expressions in the activity?” (Write the numbers in expanded form and stack them.)
1 minute: quiet think time
Share responses.
Give students access to base-ten blocks.
Activity
“Take some quiet time to try this algorithm. Check in with your partner if you have questions.”
5–7 minutes: independent work time
If students have questions about the notation used to record the decomposition of a hundred or ten into more tens or ones, consider asking:
“Is there any place in the problem where you don’t have enough tens or ones?”
“How could you get more tens (or ones)?”
“How could you record a hundred being decomposed into 10 tens (or a ten decomposed into 10 ones)?”
Student Facing
Here is a subtraction algorithm you saw in an earlier lesson:
[IMG]
Try using this algorithm to find the value of each difference. Show your reasoning. Organize it so it can be followed by others.
\(283 - 159\)
\(425 - 192\)
\(639 - 465\)
\(591 - 128\)
\(832 - 575\)
Student Response
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Advancing Student Thinking
If students do not record the multiple decompositions in the last problem, consider asking:
“What units did you need to decompose in this problem?”
“Where would it make the most sense to you to record how you decomposed a hundred into more tens? A ten into more ones?”
Activity Synthesis
Select students to share their reasoning for 2–3 problems. Choose problems to focus on based on common questions that came up. Be sure to discuss the last problem, which requires decompositions of both a ten and a hundred.
For the last problem, ask: “How did you decide how to record the ten and hundred that needed to be decomposed?” (I started subtracting the ones and decomposed a ten into 10 ones so I had already crossed off the 30 and written 20. When I decomposed the hundred into tens, I just decided to write the 120 on top of the 20 like I wrote the 20 on top of the 30.)
Record the completed algorithm, showing the decompositions of tens and hundreds.
Consider asking:
“Where were there not enough tens or ones to subtract?”
“What was decomposed and how was it recorded?”
“Did you notice any places where you might have made the error we saw in Lin's work?"


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