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: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
- An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
- An angle that turns through n one-degree angles is said to have an angle measure of n degrees.
problem_activity: Activity
The purpose of this activity is to review how to create a scatter plot using technology and come up with a function to model the data. This work is similar to the work in the associated Algebra 1 lesson, but includes more explicit instructions and steps toward analyzing data and choosing an appropriate model (MP4).
Launch
Display the table of data for all to see, and ask students whether they think a linear or exponential model would be a better fit for this data. After a minute of quiet think time, ask a few students to share their reasoning.
If needed, demonstrate using graphing technology to input the given data and create a scatter plot.
If the graphing technology platform you are using allows it, consider showing students how to create sliders. In Desmos, simply type
\(y=mx+c\)
in the expressions list, and then click “all” to add sliders for both
\(m\)
and
\(c\)
. You may need to adjust the maximum value of one or both sliders to be able to use them to create a good model for this data.
Student Facing
In the spring, an agave plant sends up a flower spike. Here are some data collected from an agave plant in a garden in Tucson, AZ, starting on April 2:
[IMG]
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "day"}, {"_attributes": {"scope": "col"}, "_value": "height in inches"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "0"}, {"_value": "17"}]}, {"td": [{"_value": "1"}, {"_value": "23"}]}, {"td": [{"_value": "2"}, {"_value": "29"}]}, {"td": [{"_value": "3"}, {"_value": "37"}]}, {"td": [{"_value": "4"}, {"_value": "45"}]}, {"td": [{"_value": "5"}, {"_value": "52"}]}, {"td": [{"_value": "6"}, {"_value": "62"}]}, {"td": [{"_value": "7"}, {"_value": "70"}]}, {"td": [{"_value": "8"}, {"_value": "80"}]}]}]}]}
Use graphing technology to create a scatter plot, using days as the first coordinate and height as the second coordinate.
Would a linear or exponential model be a better fit for this data?
Create a function that is a good model for the data. If you chose an exponential model, start with the equation
\(y=a \boldcdot b^x\)
and select values for
\(a\)
and
\(b\)
. If you chose a linear model, start with the equation
\(y=mx+c\)
, and select values for
\(m\)
and
\(c\)
.
Graph your equation on that same coordinate plane as your scatter plot. Adjust the numbers you used in the equation to improve your model.
Explain what each number in your equation means in this situation.
Use your model to predict the height of the flower spike on day 10.
Describe any limitations on the domain of the function modeling the data.
Student Response
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Activity Synthesis
Display the scatter plot using technology. Explore some of the different equations students used as a model. Discuss which model is the better fit, and what makes a model a good fit. Invite students to share their responses to the last three questions.


aligns: no