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: Recognize area as an attribute of plane figures and understand concepts of area measurement.
problem_activity: Narrative
The purpose of this activity is for students to practice identifying fractional intervals along a number line. This is Stage 2 of the center activity, Number Line Scoot. This activity encourages students to count by the number of intervals (the numerator). Students have to land exactly on the last tick mark, which represents 4, to encourage them to move along different number lines. While this activity does not focus on equivalence, it gives students exposure to this idea before they work more formally with it in the next section. In the synthesis, students relate counting on a number line marked off in whole numbers to their number lines marked off in fractional-sized intervals.
It may be helpful to play a few rounds with the whole class to be sure students are clear on the rules of the game. Keep the number line game boards for center use.
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community. For example, check in after the first round of Number Line Scoot.
Supports accessibility for: Attention, Social-Emotional Functioning
Required Materials
Materials to Gather
Base-ten blocks
Number cubes
Materials to Copy
Number Line Scoot Stage 2 Gameboard
Number Line Scoot Stage 2 Directions
Required Preparation
Each group of 2 students needs a number cube.
Each student needs at least 5 base-ten cubes to use as game pieces.
Launch
Groups of 2
Give each group of 2 a gameboard, two recording sheets, a number cube, and at least 10 base-ten cubes.
“Now you will play a game where you move, by fractions, along different number lines. To start, each player places a small cube on zero on each number line. The goal of the game is to get as many small cubes as you can to the 4 on any of the number lines.”
Roll the number cube, demonstrate where to record the rolled number and move that fraction along one of the number lines.
Activity
10 minutes: partner work time
As students work, monitor for students who count by the numerator once they have chosen a number line.
Activity Synthesis
Display a gameboard with a marker on
\(\frac{3}{4}\)
.
“If I rolled a 4, and chose to move
\(\frac{4}{4}\)
, how would you count the move?” (I would count 1, 2, 3, 4.)
“How did you know you have moved
\(\frac{4}{4}\)
?” (Because each space is
\(\frac{1}{4}\)
, so I need to move 4 times.)
Display a number line marked with only 0, 1, 2, 3, 4.
“How is counting along this number line the same and different than counting along your number lines?” (On the whole number one each space is 1 so we just count 1, 2, 3, 4. On our number lines we still count the jumps, but now each space is smaller than 1 so we need the denominator to tell us the size of each space.)


aligns: no