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: 
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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^(2) + y^(2))^(2) = (x^(2 )– y^(2))^(2) + (2xy)^(2 )can be used to generate Pythagorean triples.
problem_activity: Optional activity
The mathematical purpose of this activity is for students to collect, summarize, interpret, and draw conclusions from bivariate data using scatter plots, best fit lines, residuals and correlation coefficients. Students measure the approximate lengths of the humerus bone and height of their classmates to collect data and create a linear model. The model is then used to approximate the height of an ancient human based on the length of a found humerus bone.
Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5). By collecting their own data and using a best fit line to find additional information, students are modeling with mathematics (MP4).
Launch
Arrange students in groups of 2 to 4. Present the task to students and ask students to brainstorm different ways that they could answer the question. After 2 minutes of quiet think time, ask students to share their ideas with the class. The remaining time should be used by students to collect, analyze, summarize, and interpret the data.
Speaking, Reading: MLR5 Co-Craft Questions.
Use this routine to help students further interpret and increase awareness of the language used to talk about scatter plots, best fit lines, residuals and correlation coefficients. Display the first sentence of this problem (“An anthropologist finds a fossilized humerus bone of an ancient human ancestor.”), and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the remainder of the question. Listen for and amplify any questions involving comparing bivariate data.
Design Principle(s): Maximize meta-awareness; Support sense-making
Student Facing
[IMG]
An anthropologist finds a fossilized humerus bone of an ancient human ancestor. The humerus is an arm bone running from the shoulder to the elbow. It is 24 centimeters in length. Use data from your classmates to estimate the height of this ancient human.
Student Response
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Anticipated Misconceptions
Students may find it difficult to start to answer the question. Ask students what are the variables given in the situation. Ask students if there is a way we could collect information from people in the classroom to help answer the question.
Activity Synthesis
The purpose of this discussion is for students to communicate how they used mathematics to justify their findings.
Ask students:
“How confident are you in your answer? What information helped you determine your confidence?” (Not very confident. Since the correlation coefficient is near 0.6, there is only a moderate relationship between height and humerus length. Additionally, this ancient human ancestor may have a different anatomy—for example, apes tend to have proportionally longer arms than humans do.)
“How did you use mathematics to estimate the height of the ancient human?” (First, I collected data on the height and the approximate length of the humerus of my classmates. I then made a scatter plot to determine whether or not a linear model was appropriate, and then computed a line of best fit. I substituted 24 centimeters into my line of best fit and obtained my answer.)
“Do you think that the way you measured the humerus of your classmates impacted your choice of linear model? Explain your reasoning.” (Yes, I think that I probably overestimated the bone length, because I was measuring from the outside and not the inside. I think that my model likely overestimates height.)


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