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:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

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

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
problem_activity: Activity
In the previous activity, students noticed trends in the data from the scatter plot. In this activity, the association is made more precise by looking at equations and graphs of linear models for the data to determine the slope. The numerical value of the slope is then interpreted in the context of the problem (MP2).
Launch
Remind students that earlier we looked at the price and mileage of some used cars. We saw that for these used cars, the price tends to decrease as the mileage increases. Display the scatter plot and linear model for the data.
[IMG]
Tell students that an equation for the line is
\(y=\text-0.073x+17,\!404.485\)
. From the equation we can identify the slope of the line as -0.073. Ask students to think about what that slope tells us and give quiet think time. Select 1–2 students to share their thinking. (It means that for every increase of one mile, the model predicts that the price of the car will decrease by
$
0.073.) Tell students that in this activity they will determine what the slope of the model means for three different sets of data.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organization and problem solving. For example, present only one scatter plot at a time.
Supports accessibility for: Organization; Attention
Speaking, Writing: MLR8 Discussion Supports.
Provide a sentence frame to scaffold students’ language when describing the meaning of slope in each representation. For example, “If the _________ increases by 1 _________ , the model predicts that ___________ (increases/decreases) by ___________ .”
Design Principle: Maximize meta-awareness; Optimize output (for explanation)
Student Facing
For each of the situations, a linear model for some data is shown.
What is the slope of the line in the scatter plot for each situation?
What is the meaning of the slope in that situation?
\(y=5,\!520.619x-1,\!091.393\)
[IMG]
\(y=\text-0.011x+40.604\)
[IMG]
\(y=0.59x-21.912\)
[IMG]
Student Response
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click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
The scatter plot shows the weight and fuel efficiency data used in an earlier lesson along with a linear model represented by the equation
\(y = \text-0.0114 x +41.3021\)
.
[IMG]
What is the value of the slope and what does it mean in this context?
What does the other number in the equation represent on the graph? What does it mean in context?
Use the equation to predict the fuel efficiency of a car that weighs 100 kilograms.
Use the equation to predict the weight of a car that has a fuel efficiency of 22 mpg.
Which of these two predictions probably fits reality better? Explain.
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
The purpose of this discussion is to develop a quantitative sense of trends based on linear models of the data.
Consider asking some of the following questions:
“What was the easiest way to find the slope for each situation?” (The coefficient of the
\(x\)
-coordinate in the equation.)
“Do the answers for the meaning of the slopes make sense in the contexts of the problem?” (Yes. Diamonds are usually expensive, so a 1 carat increase is likely to cost a lot more. A 1 kilogram difference in the weight of a car is not very much, so it may lower the gas mileage, but not by much. A 1 degree temperature increase is not significant, so it should not need a lot more energy to cool off a building, but some would be needed.)
“What is the difference between a positive slope and negative slope in your interpretations?” (A positive slope means both variables increase together. A negative slope means that when one variable increases, the other decreases.)
“The model for energy consumption and temperature predicted a 0.59 kilowatt hour increase in energy consumption for every 1 degree increase in temperature. Estimate how much the temperature would need to increase to raise energy consumption by 6 kilowatt hours.” (A little more than 10 degrees.)


aligns: yes