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: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
problem_activity: Optional activity
In this partner activity, students take turns matching a sequence to a definition. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
One sequence and one definition do not have matches. Students are tasked with writing the corresponding match.
Monitor for students using clear reasoning as they create a recursive definition for the sequence 18, 20, 22, 24 to share during the discussion.
Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Arrange students in groups of 2. Tell students that for each sequence, one partner finds its matching recursive definition and explains why they think it matches. The partner's job is to listen and make sure they agree. If they don't agree, the partners discuss until they come to an agreement. For the next sequence, the students swap roles. If necessary, demonstrate this protocol before students start working.
Ensure that students notice that one sequence and one definition do not have matches, and they are tasked with writing the corresponding match for each.
Conversing: MLR8 Discussion Supports.
Use this routine to support small-group discussion as students should take turns finding a match. Display the following sentence frames for all to see: "Sequence _____ and definition _____ match because . . .” and “I noticed _____, so I matched . . .” Encourage students to challenge each other when they disagree, and to press for precise mathematical language. This will help students clarify their reasoning about each match.
Design Principle(s): Support sense-making; Maximize meta-awareness
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite groups of students to find matches for at least 4 of the sequences. Chunking this task into more manageable parts may also support students who benefit from additional processing time.
Supports accessibility for: Organization; Attention; Social-emotional skills
Student Facing
Take turns with your partner to match a sequence with a recursive definition. It may help to first figure out if the sequence is arithmetic or geometric.
For each match that you find, explain to your partner how you know it’s a match.
For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
There is one sequence and one definition that do not have matches. Create their corresponding match.
Sequences:
3, 6, 12, 24
18, 36, 72, 144
3, 8, 13, 18
18, 13, 8, 3
18, 9, 4.5, 2.25
18, 20, 22, 24
Definitions:
\(G(1)=18, G(n)=\frac12 \boldcdot G(n-1), n\ge2\)
\(H(1)=3, H(n)=5 \boldcdot H(n-1), n\ge2\)
\(J(1)=3, J(n)=J(n-1)+5, n\ge2\)
\(K(1)=18, K(n)=K(n-1)-5, n\ge2\)
\(L(1)=18, L(n)=2 \boldcdot L(n-1), n\ge2\)
\(M(1)=3, M(n)=2 \boldcdot M(n-1), n\ge2\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Some students may not be sure how to begin matching terms in a sequence to a definition. Encourage them to start by picking a definition and calculating the first few terms of the sequence it represents.
Activity Synthesis
Once all groups have completed the matching, ask “How did you decide which definitions to match to sequence 3, 6, 12, 24 and sequence 18, 36, 72, 144 when they both involve doubling?” (They are both geometric with a growth factor of 2, but since they have different first terms you can use those to match the sequences to
\(M\)
and
\(L\)
.)
Next, invite previously identified students to share the recursive definition they created for sequence 18, 20, 22, 24 and their strategy for writing it.
If time allows and students need extra practice graphing functions, assign students one function each from the task statement to sketch a graph for. After work time, select students to share their sketches, displaying them for all to see and compare.


aligns: yes