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 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: 
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_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Read, write, and compare decimals to thousandths.
problem_activity: Activity
The purpose of this activity is for students to use the four operations on rational numbers solve a problem about water in a tank. The activity presents another example where negative time is used; this time to describe before a sensor starts working. Students examine the change as a separate column before using the starting point to model the draining of the tank.
Students who see that they are doing the same computations over and over and see that the structure of the expression is the same every time are expressing regularity in repeated reasoning (MP8). Monitor for different explanations for the last question.
Launch
Arrange students in groups of 2. Give students 4 minutes of quiet work time, followed by partner and whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts. For example, after students have completed the first 2-3 rows of the first table, check-in with either select groups of students or the whole class. Invite students to share how they have applied generalizations from previous lessons about using the four operations on rational numbers so far.
Supports accessibility for: Conceptual processing; Organization; Memory
Student Facing
A tank of water is being drained. Due to a problem, the sensor does not start working until some time into the draining process. The sensor starts its recording at time zero when there are 770 liters in the tank.
Given that the drain empties the tank at a constant rate of 14 liters per minute, complete the table:
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "br": [{}], "_values": ["time after sensor", "starts (minutes)"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["change in", "water (liters)"]}, {"_attributes": {"scope": "col"}, "_value": "expression"}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["water\u00a0in the", "tank (liters)"]}]}]}], "tbody": [{"tr": [{"td": [{"_value": "0"}, {"_value": "0"}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(770 + (0) (\\text-14)\\)"}]}, {"_value": "770"}]}, {"td": [{"_value": "1"}, {"_value": "-14"}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(770 + (1) \u00a0(\\text-14) \\)"}]}, {"_value": "756"}]}, {"td": [{"_value": "5"}, {"_value": "-70"}, {}, {}]}, {"td": [{"_value": "10"}, {}, {}, {}]}]}]}]}
Later, someone wants to use the data to find out how long the tank had been draining before the sensor started. Complete this table:
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "br": [{}], "_values": ["time after sensor", "starts (minutes)"]}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["change in", "water (liters)"]}, {"_attributes": {"scope": "col"}, "_value": "expression"}, {"_attributes": {"scope": "col"}, "br": [{}], "_values": ["water\u00a0in the", "tank (liters)"]}]}]}], "tbody": [{"tr": [{"td": [{"_value": "1"}, {"_value": "-14"}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(770 + (1) (\\text-14) \\)"}]}, {"_value": "756"}]}, {"td": [{"_value": "0"}, {"_value": "0"}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(770 + (0) \u00a0(\\text-14) \\)"}]}, {"_value": "770"}]}, {"td": [{"_value": "-1"}, {"_value": "14"}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "failed-conversion"}, "_value": "\\(770 + (\\text-1) \u00a0(\\text-14) \\)"}]}, {"_value": "784"}]}, {"td": [{"_value": "-2"}, {"_value": "28"}, {}, {}]}, {"td": [{"_value": "-3"}, {}, {}, {}]}, {"td": [{"_value": "-4"}, {}, {}, {}]}, {"td": [{"_value": "-5"}, {}, {}, {}]}]}]}]}
If the sensor started working 15 minutes into the tank draining, how much was in the tank to begin with?
Student Response
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Anticipated Misconceptions
The last question might be hard for students because they have had the table to support calculating the answers.  Ask students how can they use the previous entries in the table to help them calcualte the answer?  What is something they see changing in the expressions in the table that would change in this question?
Activity Synthesis
Make sure students have filled out the tables appropriately. Select students to share their reasoning for the last one.
Speaking, Representing: MLR7 Compare and Connect.
Use this routine when students share their strategies for completing the table. Ask students to consider what is the same and what is different about the structure of each expression. Draw students’ attention to the connection between representations (e.g., “Where do you see the change in water in your expression?”, "How are do repeated computations appear in the expression?"). These exchanges strengthen students’ mathematical language use and reasoning with different representations.
Design Principle(s): Support sense-making; Maximize meta-awareness


aligns: no