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 following problem or activity 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: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
problem_activity: Narrative
The purpose of this activity is for students to interpret and solve a story problem by adding or subtracting within 100. Students solve an Add To, Start Unknown problem, one of the more difficult problem types from grade 1. Students begin the activity by looking at the problem displayed, rather than in their books. At the end of the launch, students open their books and work on the problem.
Monitor for students who use methods that show adding or subtracting by place to share in the synthesis. Students who choose to use connecting cubes or base-ten blocks or who draw a diagram to represent the situation are using tools strategically (MP5). During the synthesis, invite all students to explain why these methods work using their understanding of place value.
This activity uses
MLR6 Three Reads
. Advances: reading, listening, representing. Some students may benefit from continued use of MLR6 to support reading comprehension in Activity 2.
Required Materials
Materials to Gather
Base-ten blocks
Connecting cubes
Launch
Groups of 2
Give students access to connecting cubes and base-ten blocks.
“Have you ever been on a field trip? Where did you go?”
“Did everyone on your field trip stay together the whole time or did you split into smaller groups?”
MLR6 Three Reads
Display only the story problem, without revealing the question.
“We are going to read this problem 3 times.”
1st Read: “Some students were on the bus to go to the zoo. Then 34 more students got on. Now there are 55 students on the bus.”
“What is this story about?”
1 minute: partner discussion.
Listen for and clarify any questions about the context.
2nd Read: “Some students were on the bus to go to the zoo. Then 34 more students got on. Now there are 55 students on the bus.”
“What are all the things we can count in this story?” (number of students who started the story on the bus, number of students who got on next, the total number of students on the bus, the number of buses)
30 seconds: quiet think time
2 minutes: partner discussion
Share and record all quantities.
Reveal the question.
3rd Read: Read the entire problem, including the question aloud.
“What are different ways we can solve this problem?” (We could subtract the number of students who got on the bus second from the total. We could add to the number of students who got on the bus until we get to the total.)
30 seconds: quiet think time
1–2 minutes: partner discussion
Activity
5 minutes: independent work time
Monitor for students who:
use base-ten blocks or base-ten diagrams to show adding tens to tens or ones to ones
use base-ten blocks or base-ten diagrams to show subtracting from tens or ones from ones
Student Facing
Some students were waiting on the bus to go to the zoo. Then 34 more students got on. Now there are 55 students on the bus. How many students were on the bus at first?
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Student Response
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Activity Synthesis
Invite previously identified students to share.
Record student methods using equations.
“How are these methods the same?” (They both show tens and ones. They both thought of keeping the tens with the tens and ones with the ones.)


aligns: no