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: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
problem_activity: Activity
The activity is an opportunity to practice evaluating quadratic expressions for a negative value of the variable, and choosing parameters of an equation that will result in its graph looking a certain way.
Launch
Arrange students in groups of 2. Give students two minutes of quiet work time on the first question, and ask them to check their answers with their partner before starting the second question. Call attention to the scale on the axes. Identify students who use the scale to select the parameters for their linear equation.
Student Facing
Evaluate each expression when
\(x\)
is -3.
\(x^2\)
\(\text-x^2\)
\(x^2+20\)
\(\text-x^2+20\)
For each graph, come up with an equation that the graph could represent. Verify your equation using graphing technology.
[IMG]
Student Response
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Activity Synthesis
Invite students to share various equations that each graph could represent. Use different but equally correct equations to help students generalize. For example, either
\(y=x+15\)
or
\(y=x+12\)
makes sense for graph C, because it looks like
\(y=x\)
, and is shifted up by some number between 10 and 20. So we know that the equation this graph represents is in the form
\(y=x+b\)
, where
\(b\)
is positive, even though we can’t tell its exact value from the given information.


aligns: no