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: 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 learn stage 1 of the Jump the Line center. In this stage, students take turns making strategic choices about numbers to add or subtract to reach target numbers. Students choose 3 target numbers and mark them on the number line. Both players start at the beginning of the number line. They spin all 3 spinners and decide which of the moves they want to use on their turn. Students take turns spinning and moving, trying to land exactly on the target numbers. The first player to land on 2 target numbers wins.
Required Materials
Materials to Gather
Dry erase markers
Paper clips
Sheet protectors
Materials to Copy
Jump the Line Stage 1 Gameboard
Jump the Line Stage 1 Spinners
Launch
Groups of 2
Give each group a spinner, paper clip, dry erase marker and gameboard.
Display spinners and gameboard.
“You and your partner will choose 3 target numbers and mark them on your number line.”
“Then you will take turns spinning all 3 spinners. On your turn you can decide which spin to use. Your goal is to jump to one of the numbers you and your partner marked.”
“The first player to land exactly on 2 of the target numbers wins.”
Play a round with the class, if needed.
Activity
15 minutes: partner work time
Activity Synthesis
Display a gameboard with 3 target numbers. Spin the three spinners.
“This is my gameboard and my spins. Which spin would you use? Why?”


aligns: no