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 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_neg_0

HS_0
standard_description: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
problem_activity: Narrative
The purpose of this activity is for students to use informal language and the structure of the coordinate grid to describe a given shape. Some questions may be about properties of the shape rather than its location. For example, “Is the rectangle wider than it is tall?” is a question that eliminates many shapes. As the number of shapes decreases, the location will become more important and the features of the coordinate grid will play a larger role. The synthesis gives students an opportunity to consider how the numbers in the coordinate grid can be useful to accurately describe the attributes, location, and orientation of a given shape (MP6).
Launch
Groups of 2
Activity
5 minutes: partner work time
Monitor for students who:
reference the structure of the grid in their questions
reference the numbers on the horizontal and vertical axes in their questions
use gestures to indicate horizontal or vertical gridlines
use the words horizontal or vertical
Student Facing
Play a round of Guess Which One.
Sit next to your partner.
Partner A:
Mentally choose a shape card without indicating which shape card you chose.
Partner B:
Ask yes or no questions to determine which shape card partner A has chosen.
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
E
[IMG]
F
[IMG]
G
[IMG]
H
[IMG]
I
[IMG]
J
[IMG]
K
[IMG]
L
[IMG]
Switch roles and play another round of Guess Which One.
Diego and Kiran were playing a round of Guess Which One. These are the last two shapes. What question can Kiran ask to determine which shape is the one that Diego picked?
[IMG]
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not reference the grid lines or numbers when asking questions, refer to the display from the first activity and ask, “Which words can you use to help you figure out which shape your partner chose?”
Activity Synthesis
Ask previously identified students to share their reasoning.
“How do the numbers help us locate shapes on the grid?” (I could use them to describe the lines and the points. I could also use numbers to describe the location of the shape: “Go up three. Go over 5.”)
“The gridlines with numbers on them are called
axes
. The coordinate grid has a
horizontal axis
and a
vertical axis
.”


aligns: no