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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
problem_activity: Narrative
In this activity, students reason about the relative size of decimals by locating them on a number line. As in a previous activity, they rely on their experience of locating fractions on a number line and the relationship of the decimal values relative to 0 and 1.
If desired and logistically feasible, consider carrying out the activity on a giant number line rather than on paper.
Stretch a long strip of tape across a wall, at least 8 or 10 feet long. Partition the tape into 12 equal intervals, using shorter pieces of tape as tick marks. Label the locations of 0 and 1.
Give each group of students 2–3 dot stickers, 4–5 sticky notes, and a thick marker.
Ask each group to write (on sticky notes) labels for two of the tick marks, with one sticky note for each label.
Assign each group one or two of the eight decimals in the second problem. Ask them to locate their assigned decimals on the number line, using dot stickers to mark the location and sticky notes to label them.
Action and Expression: Internalize Executive Functions.
Synthesis: Invite students to plan a strategy, including the tools they will use, for the first two steps of the activity. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, Social-Emotional Functioning
Launch
Groups of 3–4
Activity
If creating a giant number line, lead the activity as outlined in the Activity Narrative. Otherwise, ask students to work with their group on the first two problems.
Pause and discuss:
how students knew where to put each decimal
how the number line could help us see the least and greatest
“Take a few quiet minutes to complete the rest of the activity.”
5–6 minutes: independent work time
Student Facing
Label each tick mark on the number line with the number it represents.
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Here are eight numbers.
0.10
0.40
0.80
1.10
0.15
0.45
0.75
1.05
Locate and label each number on the number line.
Which number is greatest? Which is least? Explain how the number line can help determine the greatest and least numbers.
Locate and label these numbers on the number line.
0.24
0.96
0.61
1.12
0.08
[IMG]
Use two numbers from the previous questions to complete each comparison statement so that it is true.
________ is greater than _______.
________ is less than _______.
________ is the greatest number.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
Students may be unsure whether to label the tick marks between 0 and 1 in terms of tenths or hundredths, or whether to use fraction or decimal notation. Consider asking: “What labels might be helpful for locating the decimals in the activity?”
Activity Synthesis
Select students to display their completed number lines (showing the locations of five additional decimals).
Invite the class to agree or disagree with the locations of the point and discuss any disagreements.
Select other students to share their comparison statements and how they know each statement is true.


aligns: no