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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. 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.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


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

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?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: 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.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
problem_activity: Activity
In this lesson, the meaning of the words
model
and
modeling
are explained in terms of a linear model. Students are not expected to define the words, but should be comfortable understanding and using them. A model is used to predict prices for diamonds not included in the data as well as compare existing data points to the model.
Digital
Launch
Keep students in groups of 2. Allow students 5 minutes quiet work time followed by partner and whole-class discussion.
[IMG]
Show the first image for all to see. Ask students, “Which diamond do you think has the highest price? Which diamond do you think has the lowest price?” Most likely, they will guess that the largest has the highest price and the smallest has the lowest price. Validate this intuition and let them know that the size of a diamond is
one
thing that its price is based on. Tell students that the size of a diamond is commonly measured in
carats
, which is a measure of weight. (One carat is equivalent to 200 milligrams.)
[IMG]
Show the second image for all to see. Ask students, “Which diamond do you think has the higher price?” Poll the class, and ask a few students to share their reasoning. Tell students that these diamonds are the same size, but they are not the same price. The price of a diamond is not just based on size, but also on how many flaws are inside the stone. Since the diamond on the right has fewer flaws (which makes it more sparkly), it has a higher price than the diamond on the left.
Tell students, “You will look at some data for the prices of diamonds of different sizes. You have used mathematics to analyze real-world situations, identifying variables in a situation and describing their relationships mathematically. This process is called
modeling,
and the mathematical description is called a
model
. Sometimes you made assumptions about the situation or ignored some features so that the model would be simpler.”
Action and Expression: Develop Expression and Communication
. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their ideas. For example, “It looks like…” and “We are trying to…”
Supports accessibility for: Language; Organization
Speaking: MLR8 Discussion Supports.
Provide sentence frames to support students as they work with their partner and explain their reasoning. For example, “I think ____ because _____ .” or “I (agree/disagree) because ______ .”
Design Principle(s): Support sense-making; Optimize output for (explanation)
Student Facing
Here is a table that shows weights and prices of 20 different diamonds.
| weight (carats) | actual price (dollars) | predicted price (dollars) |
|-----------------|------------------------|---------------------------|
|        1        |         3,772          |           4,429           |
|        1        |         4,221          |           4,429           |
|        1        |         4,032          |           4,429           |
|        1        |         5,385          |           4,429           |
|      1.05       |         3,942          |           4,705           |
|      1.05       |         4,480          |           4,705           |
|      1.06       |         4,511          |           4,760           |
|       1.2       |         5,544          |           5,533           |
|       1.3       |         6,131          |           6,085           |
|      1.32       |         5,872          |           6,195           |
|      1.41       |         7,122          |           6,692           |
|       1.5       |         7,474          |           7,189           |
|       1.5       |         5,904          |           7,189           |
|      1.59       |         8,706          |           7,686           |
|      1.61       |         8,252          |           7,796           |
|      1.73       |         9,530          |           8,459           |
|      1.77       |         9,374          |           8,679           |
|      1.85       |         8,169          |           9,121           |
|       1.9       |         9,541          |           9,397           |
|      2.04       |         9,125          |          10,170           |
The scatter plot shows the prices and weights of the 20 diamonds together with the graph of
\(y = 5,\!520x- 1,\!091\)
.
The function described by the equation
\(y = 5,\!520x- 1,\!091\)
is a
model
of the relationship between a diamond’s weight and its price.
This model
predicts
the price of a diamond from its weight. These predicted prices are shown in the third column of the table.
Two diamonds that both weigh 1.5 carats have different prices. What are their prices? How can you see this in the table? How can you see this in the graph?
The
model
predicts that when the weight is 1.5 carats, the price will be
$
7,189. How can you see this in the graph? How can you see this using the equation?
One of the diamonds weighs 1.9 carats. What does the model predict for its price? How does that compare to the actual price?
Find a diamond for which the model makes a very good prediction of the actual price. How can you see this in the table? In the graph?
Find a diamond for which the model’s prediction is not very close to the actual price. How can you see this in the table? In the graph?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Keep students in groups of 2. Allow students 5 minutes quiet work time followed by partner and whole-class discussion.
[IMG]
Show the first image for all to see. Ask students, “Which diamond do you think has the highest price? Which diamond do you think has the lowest price?” Most likely, they will guess that the largest has the highest price and the smallest has the lowest price. Validate this intuition and let them know that the size of a diamond is
one
thing that its price is based on. Tell students that the size of a diamond is commonly measured in
carats
, which is a measure of weight. (One carat is equivalent to 200 milligrams.)
[IMG]
Show the second image for all to see. Ask students, “Which diamond do you think has the higher price?” Poll the class, and ask a few students to share their reasoning. Tell students that these diamonds are the same size, but they are not the same price. The price of a diamond is not just based on size, but also on how many flaws are inside the stone. Since the diamond on the right has fewer flaws (which makes it more sparkly), it has a higher price than the diamond on the left.
Tell students, “You will look at some data for the prices of diamonds of different sizes. You have used mathematics to analyze real-world situations, identifying variables in a situation and describing their relationships mathematically. This process is called
modeling,
and the mathematical description is called a
model
. Sometimes you made assumptions about the situation or ignored some features so that the model would be simpler.”
Action and Expression: Develop Expression and Communication
. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their ideas. For example, “It looks like…” and “We are trying to…”
Supports accessibility for: Language; Organization
Speaking: MLR8 Discussion Supports.
Provide sentence frames to support students as they work with their partner and explain their reasoning. For example, “I think ____ because _____ .” or “I (agree/disagree) because ______ .”
Design Principle(s): Support sense-making; Optimize output for (explanation)
Student Facing
Here is a table that shows weights and prices of 20 different diamonds.
| weight (carats) | actual price (dollars) | predicted price (dollars) |
|-----------------|------------------------|---------------------------|
|        1        |         3,772          |           4,429           |
|        1        |         4,221          |           4,429           |
|        1        |         4,032          |           4,429           |
|        1        |         5,385          |           4,429           |
|      1.05       |         3,942          |           4,705           |
|      1.05       |         4,480          |           4,705           |
|      1.06       |         4,511          |           4,760           |
|       1.2       |         5,544          |           5,533           |
|       1.3       |         6,131          |           6,085           |
|      1.32       |         5,872          |           6,195           |
|      1.41       |         7,122          |           6,692           |
|       1.5       |         7,474          |           7,189           |
|       1.5       |         5,904          |           7,189           |
|      1.59       |         8,706          |           7,686           |
|      1.61       |         8,252          |           7,796           |
|      1.73       |         9,530          |           8,459           |
|      1.77       |         9,374          |           8,679           |
|      1.85       |         8,169          |           9,121           |
|       1.9       |         9,541          |           9,397           |
|      2.04       |         9,125          |          10,170           |
The scatter plot shows the prices and weights of the 20 diamonds together with the graph of
\(y = 5,\!520x- 1,\!091\)
.
[IMG]
The function described by the equation
\(y = 5,\!520x- 1,\!091\)
is a
model
of the relationship between a diamond’s weight and its price.
This model
predicts
the price of a diamond from its weight. These predicted prices are shown in the third column of the table.
Two diamonds that both weigh 1.5 carats have different prices. What are their prices? How can you see this in the table? How can you see this in the graph?
The model predicts that when the weight is 1.5 carats, the price will be
$
7,189. How can you see this in the graph? How can you see this using the equation?
One of the diamonds weighs 1.9 carats. What does the model predict for its price? How does that compare to the actual price?
Find a diamond for which the model makes a very good prediction of the actual price. How can you see this in the table? In the graph?
Find a diamond for which the model’s prediction is not very close to the actual price. How can you see this in the table? In the graph?
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
The goal of this discussion is to help students understand the relationship between the data and a linear model of the data.
To highlight there relationship, ask:
"What does a point in the scatter plot represent?" (The
actual
weight and price of a diamond.)
"What does the line represent?" (The
predicted
price of a diamond based on its weight.)
"What does it mean when a point is close to the line? When it is far away from the line?" (When it is close, the model predicts the price well. The farther away in the vertical direction, the worse the prediction.)
"How can you use the graph to predict the price of a diamond that weighs 1.1 carats? How can you use the equation?" (Find the point on the line that lines up with
\(x = 1.1\)
or substitute
\(x = 1.1\)
into the model equation.)


correct_option_index: 1

3