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: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Optional activity
This activity gives students a chance to recall and use various ratio strategies in the context of a voting problem. Two classes voted on a yes or no question. Both classes voted yes. Students are asked to determine which class was more in favor (“yessier”). Students need to make sense of the invented word “yessier” by thinking about how it might be quantified (MP1, MP2).
Monitor for students who use different ways to make sense of the problem.
Launch
Arrange students in groups of 2–4. Ask students to use the mathematical tools they know to answer the question.
Student Facing
Two sixth-grade classes, A and B, voted on whether to give the answers to their math problems in poetry. The “yes” choice was more popular in both classes.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}}, {"_attributes": {"scope": "col"}, "_value": "yes"}, {"_attributes": {"scope": "col"}, "_value": "no"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "class A"}], "td": [{"_value": "24"}, {"_value": "16"}]}, {"th": [{"_attributes": {"scope": "col"}, "_value": "class B"}], "td": [{"_value": "18"}, {"_value": "9"}]}]}]}]}
Was one class more in favor of math poetry, or were they equally in favor? Find three or more ways to answer the question.
Student Response
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Anticipated Misconceptions
Students may not understand the question. The word “yessy” was invented by other students solving a similar problem. It is not standard English.
If students do not understand what comparing the two classes means, give a more extreme example, such as comparing 20 to 1 with 11 to 10. The 20 to 1 class is much more yessy because almost everyone said yes. The other class had almost equal yesses and nos.
Activity Synthesis
The situation is mathematically the same as other rate comparison problems, such as comparing the tastes or colors of two mixtures.
Invite several students to present different methods, at least one who used a ratio of yesses to nos, and another who used a ratio of yesses to all students. Make sure to present a solution using percentages.
If more than a few students did not use multiplicative techniques (for example, if they compared only the yesses, or subtracted to find how many more yesses than nos) remind them of the rate comparisons they did earlier in the year, in which they could check by tasting a drink mixture or looking at the color of a paint mixture.
Speaking, Listening, Representing: MLR2 Collect and Display.
Use this routine to display examples of the different methods students used to determine which class was “yessier." Circulate and collect examples of formal and informal language, calculations, tables, or other writting. Ask students to compare and contrast percentage calculations with fractions and equivalent ratios.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


aligns: no