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: Understand ordering and absolute value of rational numbers.

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
problem_activity: Activity
The purpose of this task is for students to develop their understanding of the
\(|x|\)
notation in familiar contexts. They should build their understanding that
\(|x|\)
represents the distance from zero to
\(x\)
and that
\(|\text-x|\)
and
\(|x|\)
are equal.
Launch
Allow students 10 minutes quiet work time followed by whole-class discussion.
Student Facing
A part of the city of New Orleans is 6 feet below sea level. We can use “-6 feet” to describe its elevation, and “
\(|\text-6|\)
feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?
25 feet
\(|25|\)
feet
-8 feet
\(|\text-8|\)
feet
The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.
We write “
\(\text-5^\circ \text{C}\)
” to describe a temperature that is 5 degrees Celsius below freezing point and “
\(5^\circ \text{C}\)
” for a temperature that is 5 degrees above freezing. In this context, what do each of the following numbers describe?
\(1^\circ \text{C}\)
\(\text-4^\circ \text{C}\)
\(|12|^\circ \text{C}\)
\(|\text-7|^\circ \text{C}\)
Which temperature is colder:
\(\text-6^\circ \text{C}\)
or
\(3^\circ \text{C}\)
?
Which temperature is closer to freezing temperature:
\(\text-6^\circ \text{C}\)
or
\(3^\circ \text{C}\)
?
Which temperature has a smaller absolute value? Explain how you know.
Student Response
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Student Facing
Are you ready for more?
At a certain time, the difference between the temperature in New York City and in Boston was 7 degrees Celsius. The difference between the temperature in Boston and in Chicago was also 7 degrees Celsius. Was the temperature in New York City the same as the temperature in Chicago? Explain your answer.
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
To summarize students’ work, consider displaying the following diagram and these four expressions. Give students a minute to study the diagram and match each letter on the diagram to an appropriate expression.
-4 feet
\(|{15}|\)
feet
\(|{\text -4}|\)
feet
15 feet
[IMG]
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of: absolute value of a number, elevation, sea level, less than, greater than.
Supports accessibility for: Conceptual processing; Language; Memory
Representing, Speaking: MLR7 Compare and Connect
. To help students connect the numerical values with the diagram in the activity synthesis, provide students phrases that also connect to the situation (e.g., “4 feet below sea level,” “15 feet from sea level,” “4 feet from sea level,” and “15 feet above sea level”). Emphasize the language needed to say what the numerical values mean and how those values connect to the diagram and the phrases.
Design Principle(s): Maximize meta-awareness


correct_option_index: 0