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 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: 
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_neg_0

7

fl_problem_001894_pos_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 add and subtract multiples of 10 and 100 within 1,000. Students interpret situations with base-ten blocks and base-ten diagrams and use equations to represents sums and differences. In the activity synthesis, students relate the situation, base-ten diagram, and equation and notice, through repeated reasoning, that when adding and subtracting, one can add or subtract hundreds and hundreds and tens and tens (MP7, MP8).
MLR7 Compare and Connect.
Synthesis: Lead a discussion comparing, contrasting, and connecting their different ways of representing the value of Mai and Lin’s blocks together. Ask, “How do these different representations show the same information?” “How are they different?”
Advances: Representing, Conversing
Representation: Access for Perception.
Invite students to act out the scenario of giving and taking hundreds on a number line. Discuss the individual jumps of 100 if a jump of 400 is too much to begin.
Supports accessibility for: Conceptual Processing, Language, Organization
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“These students were using base-ten blocks to find the value of sums and differences.”
“For each problem, represent the student’s value in a way that makes sense to you. You can use base-ten blocks, diagrams, or equations.”
10 minutes: partner work time
For Priya and Jada’s blocks, monitor for students who:
write equations to show the sums and differences.
use base-ten diagrams to show subtraction.
Student Facing
Mai has 2 hundreds, 2 tens, and 3 ones. Lin has 4 hundreds.
Represent their values with base-ten blocks or diagrams.
What is the value of their blocks altogether? Show your thinking.
Andre has 4 hundreds, 2 tens, and 8 ones.
Represent his value with base-ten blocks or diagrams.
Andre gives 2 hundreds to Clare.
What is the value of his blocks now? Show your thinking.
Diego has 6 tens. Tyler has 8 hundreds, 3 tens, and 6 ones.
What is the value of their blocks together? Show your thinking.
Elena has 5 hundreds, 7 tens, and 2 ones. She gives 2 tens to Kiran.
What is the value of her blocks now? Show your thinking.
Priya has 6 hundreds, 5 tens, and 8 ones. Han gives her 3 hundreds.
What is the value of her blocks now? Show your thinking.
Jada has 4 hundreds, 8 tens, and 2 ones. She gives 3 hundreds to Noah.
What is the value of her blocks now? Show your thinking.
Student Response
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Advancing Student Thinking
If students draw diagrams that do not match the situation or write equations that are not true, consider asking:
“Can you explain what you did?”
“Do you notice any patterns when you add or subtract hundreds and hundreds? Tens and tens?”
Activity Synthesis
Invite a student to share their representation and equation for Jada’s blocks. If no students use a base-ten diagram, select a student to share how they use base-ten blocks, and use a base-ten diagram to record their steps.
“How does the base-ten diagram show Jada’s blocks?” (The blocks show how many Jada started with. The lines show the 3 hundreds that were taken away.)
Display
\(482 - 300 = 182\)
“How does the equation show Jada’s blocks?” (482 is what Jada started with and 300 is the 3 hundreds she gave away. 182 is how much she has left.)


aligns: no