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: 
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_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
problem_activity: Activity
The purpose of this activity is for students to practice identifying the parts of a linear equation that affect specific features of its graph, specifically the slope and
\(y\)
-intercept. This will be useful when students make connections between two-variable linear equations and their graphs and situations that they represent in an associated Algebra 1 lesson.
Student Facing
For each equation, identify the slope and
\(y\)
-intercept of its graph.
\(y = 3x-8\)
\(y = 10-2x\)
\(y = \frac{x}{2} + 1\)
\(y + 1 = 9x\)
\(y = \frac{1}{3}(9x + 12)\)
Student Response
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Activity Synthesis
Discuss the slopes and
\(y\)
-intercepts and how they can be used. Here are discussion questions:
"How do you find the slope and
\(y\)
-intercept for the graph of a linear equation written in standard form like
\(\text-3x+y=\text-8\)
?" (Substitute 0 for
\(x\)
and solve for
\(y\)
.)
"The rate of change in a situation corresponds to what part of the graph?" (The rate of change corresponds to the slope of a graph.)
"Why is it useful to know the
\(y\)
-intercept and slope?" (The
\(y\)
-intercept and slope can make it very easy to create a graph from an equation because we know the key features. Also, they are useful to know in understanding a situation and the relationships between each quantity involved.)


aligns: yes