few_shots: 
Example 1:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Concept/skill: 
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Answer: 
Yes. This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.

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:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

Answer: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

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6

fl_problem_001097_neg_0

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fl_problem_001392_pos_0

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standard_description: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
problem_activity: Narrative
The purpose of this activity is for students to solve a variety of Add to and Take from Result or Change Unknown story problems. Students solve the story problems any way they choose and write an equation that matches the story and has a box around the answer to the question. During the activity synthesis, students consider the different ways to write equations for a story problem.
MLR8 Discussion Supports.
Synthesis: For each method that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Social-Emotional Functioning, Attention
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
"We are going to solve some more story problems about books other kids like to read."
Activity
Read the problems.
5 minutes: independent work time
5 minutes: partner discussion
Student Facing
Mai has read 3 books about dogs.
Diego gives her 4 more books to read.
How many books about dogs will Mai read all together?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Noah has 4 books of poetry.
His sister gives him some more books.
Now he has 10 books of poetry.
How many books did his sister give him?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Tyler has 7 books about spiders.
He gives 3 of his books to Kiran.
How many books does Tyler have left?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Lin has 5 books about outer space.
Her teacher gives her some more books.
Now she has 10 books about outer space.
How many books did Lin's teacher give her?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share the equation for each problem.
"Why is the answer in different places in our equations?" (Because in some stories we know the two numbers to add together and then the answer is the total. In other problems we know the starting number and the total and the answer is the other number we added.)


aligns: no