few_shots: 
Example 1:
Concept/skill: 
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.

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.


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

Example 2:
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.

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} $

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

Example 3:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

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?


Answer: 
Yes. 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.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

im_task_000157_pos_0

3

fl_problem_000674_pos_0

5
standard_description: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
problem_activity: Activity
The purpose of the task is for students to compare signed numbers in a real-world context and then use inequality signs accurately with negative numbers (MP2). The context should help students understand “less than” or “greater than” language. Students evaluate and critique another's reasoning (MP3).
Launch
Allow students 5–6 minutes quiet work time followed by whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Some students may benefit from access to partially completed or blank number lines. Consider preparing blank number lines with just the tick marks to get students started.
Supports accessibility for: Visual-spatial processing; Organization
Student Facing
Here are the low temperatures, in degrees Celsius, for a week in Anchorage, Alaska.
|     day     | Mon | Tues | Weds | Thurs | Fri | Sat | Sun |
|-------------|-----|------|------|-------|-----|-----|-----|
| temperature |     |      |      |       |     |     |     |
Plot the temperatures on a number line. Which day of the week had the lowest low temperature?
The lowest temperature ever recorded in the United States was -62 degrees Celsius, in Prospect Creek Camp, Alaska. The average temperature on Mars is about -55 degrees Celsius.
Which is warmer, the coldest temperature recorded in the USA, or the average temperature on Mars? Explain how you know.
Write an inequality to show your answer.
On a winter day the low temperature in Anchorage, Alaska, was -21 degrees Celsius and the low temperature in Minneapolis, Minnesota, was -14 degrees Celsius.
Jada said, “I know that 14 is less than 21, so -14 is also less than -21. This means that it was colder in Minneapolis than in Anchorage.”
Do you agree? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Another temperature scale frequently used in science is the
Kelvin scale
. In this scale, 0 is the lowest possible temperature of anything in the universe, and it is -273.15 degrees in the Celsius scale. Each
\(1\text{ K}\)
is the same as
\(1^\circ\text{C}\)
, so
\(10\text{ K}\)
is the same as
\(\text-263.15^\circ\text{C}\)
.
Water boils at
\(100^\circ \text{C}\)
. What is this temperature in
\(\text{K}\)
?
Ammonia boils at
\(\text-35.5^\circ \text{C}\)
. What is the boiling point of ammonia in
\(\text{K}\)
?
Explain why only positive numbers (and 0) are needed to record temperature in
\(\text{K}\)
.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Some students may have difficulty comparing numbers on the negative side of the number line. Have students plot the numbers on a number line in order to sequence them from least to greatest. Make it evident that temperatures become warmer (i.e., greater) as they move from left to right on the number line.
Activity Synthesis
Ask students to explain how they could tell which of the two negative numbers was greater in problem 2. After gathering 1 or 2 responses, display the following image for all to see:
[IMG]
Explain to students that as we go to the right on the number line, we can think of the temperature as getting hotter, and as we go to the left, we can think of the temperature as getting colder. Numbers don’t always describe temperature, though. So we use the word “greater” to describe a number that is farther to the right, and “less” to describe numbers that are farther to the left. For example, we would write
\(6 > \text-50\)
and say “6 is greater than -50 because it is farther to the right on the number line.” Equivalently, we could write
\(\text-50 < 6\)
and say “-50 is less than 6 because -50 is farther to the left on the number line.”
Ask students to make up their own list of negative numbers and plot on a number line. Then ask them to write several inequality statements with their numbers. As time allows, have students share one inequality statement with the class to see if all agree that it is true. If time allows, have students swap their list with a partner to plot and check their partner’s number lines and inequality statements.
Speaking: MLR7 Compare and Connect.
Use this routine to support students’ understanding of both the language and the symbolic notation of inequalities. Ask students to consider what is the same and what is different between the following sentences: “6 degrees is warmer than -50 degrees,” “6 is greater than -50,” and “
\(6 > \text-50\)
.” This helps students make the connection between the language of the context, the written inequality statement and the symbolic inequality statement.
Design Principle(s): Optimize output (for comparison); Maximize meta-awareness


aligns: no