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 to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

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_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
problem_activity: Narrative
The purpose of this activity is for students to practice finding the value of division expressions using any strategy that makes sense to them. They may divide the dividend into equal groups or use the divisor to multiply up to the given dividend. They may choose to represent the division or multiplication with base-ten blocks or by drawing diagrams.
During the synthesis, highlight strategies that rely on place value, properties of operations, and the relationship between multiplication and division (MP7).
Representation: Develop Language and Symbols.
Synthesis: Make connections between representations visible. Elicit from students the connections between the different strategies and representations shared by students.
Supports accessibility for: Visual-Spatial Processing, Conceptual Processing
Required Materials
Materials to Gather
Base-ten blocks
Materials to Copy
Centimeter Grid Paper - Standard
Launch
Groups of 2
Give students access to base-ten blocks and grid paper.
Activity
“Find the value of each quotient. You can use whatever strategy or representation you prefer.”
8–10 minutes: independent work time
Monitor for a variety of strategies and representations. Identify students to share in the synthesis.
“Share your favorite way to divide with your partner.”
2–3 minutes: partner discussion
Student Facing
Find the value of each quotient. Explain or show your reasoning. Organize it so it can be followed by others.
\(80 \div 5\)
\(68 \div 4\)
\(91 \div 7\)
If you have time: Eighty-four students on a field trip are put into groups. Each group has 14 students. How many groups are there?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Have previously selected students share their responses. Display or record the strategies and representations students use.
For each problem, consider polling the class on the strategy they used.


aligns: no