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: 
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 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_neg_0

HS_0
standard_description: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
problem_activity: Narrative
The purpose of this activity is for students to practice adding a one-digit number and a two-digit number in a way that makes sense to them. Students may choose to use methods shared in the previous activity. Give half of the class one-digit numbers and the other half two-digit numbers. Students pair up to create a sum with a two-digit number and a one-digit number. In some problems, the sum will require composing a ten when adding ones to ones. Monitor for students who share ways they make a new ten with connecting cubes or drawings to share in the synthesis.
When students choose a method to add based on the pair of numbers they are adding, they make use of structure and apply regularity in reasoning (MP7, MP8). This could mean counting on when the 1-digit number is small, adding the ones when there is no new ten, and adding on to make a ten if needed.
MLR8 Discussion Supports.
Synthesis: For each method that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking.
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Materials to Copy
Add Em' Up Cards (2-digit and 1-digit numbers to 100)
Required Preparation
Create a set of cards from the blackline master for the class.
Launch
Groups of 2
Give students access to connecting cubes in towers of 10 and singles.
Give half of the students one-digit number cards and half of the students two-digit number cards.
Display the student workbook page with the practice round.
“Each person has a card with a number on it. You will find a partner and find the sum of your two numbers. One student should have a one-digit number and the other should have a two-digit number. Let's do one round together.”
Invite one student with each kind of card to share their number.
“Find the sum of the numbers. Show your thinking using drawings, numbers, or words. Then write an equation that shows the value you found.”
2 minutes: independent work time
Share an equation that could be used.
“Now we will all play a few rounds.”
Activity
“Find a partner and find the sum of your numbers.”
5 minutes: partner work time
“Switch cards with your partner and find a new partner.”
Repeat as time allows.
Monitor for students whose sum:
does not require composing a new ten.
requires composing a new ten when adding ones and ones.
Student Facing
Practice Round:
Show your thinking using drawings, numbers, or words.
Equation: __________________________________
[IMG]
Round 1:
Show your thinking using drawings, numbers, or words.
Equation: __________________________________
Round 2:
Show your thinking using drawings, numbers, or words.
Equation: __________________________________
Round 3:
Show your thinking using drawings, numbers, or words.
Equation: __________________________________
Round 4:
Show your thinking using drawings, numbers, or words.
Equation: __________________________________
Round 5:
Show your thinking using drawings, numbers, or words.
Equation: __________________________________
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Invite previously identified students to share.
After each student shares, ask “Why did you choose this method?” (Since I was adding only 3, I could count on quickly. The number 9 would take too long to count on so I broke it apart to make a new ten and then added the rest.)


aligns: no