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: 
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_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
problem_activity: Activity
In the warm-up, students learned that measurement error can result from the level of precision in a measuring device. In this activity, students learn about how real-world limitations on humans using measuring devices can introduce measurement errors. They discuss possible sources of error and express the error both as an amount and as a percentage. This is their first introduction into the concept of measurement error and how we use that to calculate percent error.
Launch
Keep students in groups of 2. Tell students that a soccer field is 120 yards long and ask them how they can measure that length using a 30-foot-long tape measure. (Note the use of two different units of measure, here.) If not mentioned by students, suggest measuring off 30 feet, making a mark, measuring off another 30 feet, and so on. Ask the class if they would all get exactly the same answer by this method. Tell students they are going to think more deeply about a specific measurement made by a person. Give the students 1–2 minutes of quiet work time to calculate the amount of the error and the percent error followed by partner and whole-group discussions.
Student Facing
A soccer field is 120 yards long. Han measures the length of the field using a 30-foot-long tape measure and gets a measurement of 358 feet, 10 inches.
What is the amount of the error?
Express the error as a percentage of the actual length of the field.
Student Response
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Anticipated Misconceptions
If students fail to see the need for converting units of measure, ask them how many feet are in 120 yards? How many inches?
Activity Synthesis
Ask students, "What is a possible cause of the error?" Possible reasons include:
He did not position the tape measure precisely every time he measured another 30 feet.
He didn't go in a completely straight line. (Although this would result in a longer measurement.)
Han did not correctly use the measuring tape.
Ask a few students to share their solutions for the last problem.
Explain to students,
measurement error
is the positive difference between the measurement and the actual value. The
percent error
is the error expressed as a percentage of the actual value. We always use a positive number to express percent error and, when appropriate, use words to describe whether the measurement is greater than or less than the actual value. In this case, we might say that the measured length was less than the actual length with a percent error of 0.32%.
Ask, "When might percent error be more useful than measurement error?" If needed, give an example of measuring a student's height and being incorrect by an inch versus measuring the height of a skyscraper and being incorrect by an inch. Although the measurement error is the same (1 inch), the percent error is very different since the 1 inch difference is significantly more important when measuring shorter distances.
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of: measurement error and percent error.
Supports accessibility for: Memory; Language
Speaking: MLR7 Compare and Connect.
Use this routine when students present their strategies for calculating the percent error. Ask students to consider what is the same and what is different about each approach. Draw students' attention to the associations between the measurement, measurement error, and percent error. As students share what they noticed between the strategies, revoice their statements using the terms “measurement error” and “percent error.” These exchanges can strengthen students' mathematical language use and reasoning based on measurement errors.
Design Principle(s): Maximize meta-awareness


aligns: no