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: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
This activity gives students opportunities to practice explaining or showing whether two fractions are equivalent. Students may do so using a visual representation, by reasoning about the number and size of the fractional parts in each fraction, or by thinking about multiplicative relationships between the numbers in the given fractions.
Students participate in a gallery walk in which they generate equivalent fractions for the numbers on the posters. Students visit at least two of six posters (or as many as time permits)—at least one poster with two fractions (posters A–C) and one poster with three fractions (posters D–F). Here are the sets shown on the blackline master:
A
​​​​​
\(\frac{2}{10}\)
,
\(\frac{20}{100}\)
B
\(\frac{6}{4}\)
,
\(\frac{18}{12}\)
C
\(\frac{3}{5}\)
,
\(\frac{60}{100}\)
D
​​​​​​
\(\frac{1}{4}\)
,
\(\frac{3}{12}\)
,
\(\frac{30}{100}\)
E
\(\frac{15}{6}\)
,
\(\frac{7}{4}\)
,
\(\frac{30}{12}\)
F
\(\frac{7}{3}\)
,
\(\frac{21}{10}\)
,
\(\frac{28}{12}\)
Because at the posters with two fractions (A–C) students would need to generate an equivalent fraction that hasn’t already been written by others, generating equivalent fractions becomes more difficult as the activity goes on. Consider using this to differentiate for students who may need an additional challenge: start them at the posters with three fractions (D–F).
MLR8 Discussion Supports.
Synthesis. Display sentence frames to support whole-class discussion: “I agree because . . .” and “I disagree because . . . .”
Advances: Speaking, Conversing
Required Materials
Materials to Gather
Sticky notes
Materials to Copy
How Do You Know
Required Preparation
Each group needs 4 sticky notes.
Launch
Groups of 3–4
Give each group 4 sticky notes
Read the task statement as a class. Solicit clarifying questions from students.
Invite a couple of students to recap the directions in their own words or to demonstrate the process, if helpful.
Consider assigning each group a starting poster and giving directions for rotation.
Activity
10 minutes: gallery walk
Tell students who are visiting posters A–C that they could leave feedback about the fraction on a sticky note if they disagree that it is equivalent to the fractions on the poster. They should include their name and be prepared to explain how they know.
Student Facing
Around the room you will find six posters, each showing either two or three fractions.
With your group, visit at least two posters: one with two fractions and one with three fractions.
[IMG]
For the set of 2 fractions:
Explain or show how you know the fractions are equivalent.
Write a new equivalent fraction on a sticky note and add it to the poster. Think of a fraction that hasn’t already been written by someone else.
We visited poster __________, which shows __________ and __________.
New equivalent fraction: __________
For the set of 3 fractions:
Identify 2 fractions that are equivalent. Explain your reasoning.
We visited poster __________, which shows __________, __________, and __________.
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
See lesson synthesis.


aligns: no