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 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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
problem_activity: Narrative
The purpose of this activity is for students to analyze pairs of fractions to determine if they are equivalent. Students may use any representation that makes sense to them. Students will create a visual display and have a gallery walk to consider the different ways of looking for equivalence. Highlight representations such as diagrams and number lines, which will support students as they learn to compare fractions with the same numerator or denominator in this section.
This activity uses
MLR7 Compare and Connect. Advances: representing, conversing
Engagement: Develop Effort and Persistence.
Invite students to generate a list of shared expectations for group work. Record responses on a display and keep visible during the activity.
Supports accessibility for: Social-Emotional Functioning
Required Materials
Materials to Gather
Materials for creating a visual display
Launch
Groups of 2
“Decide if these pairs of fractions are equivalent and show your thinking for each one. You can use any representation that makes sense to you.”
Activity
3–5 minutes: independent work time
“Share your ideas with your partner.”
2–3 minutes: partner discussion
MLR7 Compare and Connect
“Work with your partner to create a visual display that shows your thinking about
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
. You may want to include details such as notes, diagrams, drawings, and so on, to help others understand your thinking.”
Give students materials for creating a visual display.
2–5 minutes: partner work time
5–7 minutes: gallery walk
Student Facing
Are these fractions equivalent? Show your thinking using diagrams, symbols, or other representations.
\(\frac{1}{2}\)
and
\(\frac{1}{3}\)
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
\(\frac{3}{4}\)
and
\(\frac{6}{8}\)
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
If students don’t determine whether or not fractions are equivalent, consider asking:
“What do you know about these fractions?”
“How could you use your fraction strips or diagrams to decide if they are equivalent?”
Activity Synthesis
“What are the different representations we can use to decide if
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
are equivalent?” (diagrams, number lines)
“How did each representation show that
\(\frac{4}{6}\)
and
\(\frac{5}{6}\)
are not equivalent?” (In the diagram, you can see that
\(\frac{5}{6}\)
has more space shaded. On the number line, they are not at the same location.)


aligns: no