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: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
problem_activity: Activity
The purpose of this lesson is to increase fluency in solving equations. Students will solve equations individually and then compare differing, though accurate, solution paths in order to compare their work with others. This will help students recognize that while the final solution will be the same, there is more than one path to the correct answer that uses principles of balancing equations learned in previous lessons.
Launch
Arrange students in groups of 3–4. Give students quiet think time to complete the activity and then tell groups to share how they solved the equations for
\(x\)
and discuss the similarities and differences in their solution paths.
Representation: Internalize Comprehension.
Activate or supply background knowledge about solving equations. Encourage students to use previously solved equations as guidelines to determine appropriate steps.
Supports accessibility for: Memory; Conceptual processing
Representing, Conversing: MLR2 Collect and Display.
As groups discuss their work, circulate and listen for the language students describe the similarities and differences in their solution paths. Write down different solution paths that led to the same result in a visual display. Consider grouping words and phrases used for each step in different areas of the display (e.g., “multiply first”, “divide first”, “subtract
\(x\)
from the right”, “add
\(x\)
from the left”). Continue to update the display as students move through the activity, and remind them to borrow from the display while discussing with their group. This will help students develop their mathematical language around explaining different solution paths to solving equations.
Design Principle(s); Maximize meta-awareness
Student Facing
Solve these equations for
\(x\)
.
1.
\(\frac{12+6x}{3}=\frac{5-9}{2}\)
2.
\(x-4=\frac13(6x-54)\)
3.
\(\text-(3x-12)=9x-4\)
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
I have 24 pencils and 3 cups. The second cup holds one more pencil than the first. The third holds one more than the second. How many pencils does each cup contain?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Students should take away from this activity the importance of using valid steps to solve an equation over following a specific solution path. Invite students to share what they discussed in their groups. Consider using some of the following prompts:
“How many different ways did your group members solve each problem?”
“When you compared solution paths, did you still come up with the same solution?” (Yes, even though we took different paths, we ended up with the same solutions.)
“How can you make sure that the path you choose to solve an equation is a valid path?” (I can use the steps we discovered earlier when we were balancing: adding the same value to each side, multiplying (or dividing) by the same value to each side, distributing and collecting like terms whenever it is needed.)
“What are some examples of steps that will not result in a valid solution?” (Performing an action to only one side of an equation and distributing incorrectly will give an incorrect solution.)


aligns: no