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: Solve linear equations in one variable.

Analyze and solve pairs of simultaneous linear equations.
problem_activity: Activity
Students represent a scenario with an equation and use the equation to find solutions. They create a graph (either with a table of values or by using two intercepts), interpret points on the graph, and interpret points not on the graph (MP2).
Launch
Allow about 10 minutes quiet think time for questions 1 through 4, then have students work with a partner to discuss questions 4 and 5. Look for students who define the variables or label the axes differently. This can be an opportunity to discuss the importance of defining what quantities your variables represent and that different graphs can represent the same information.
Speaking, Listening: MLR2 Collect and Display.
Listen for and record the language students use to discuss the statement “List two ways that you can tell if a pair of numbers is a solution to an equation.” Organize and group similar strategies in the display for students to refer back to throughout the lesson. For example, group strategies that reference the equation in one area and strategies that reference the graph in another area. This will help students solidify their understanding about solutions to an equation.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
The Fabulous Fish Market orders tilapia, which costs
$
3 per pound, and salmon, which costs
$
5 per pound. The market budgets
$
210 to spend on this order each day.
What are five different combinations of salmon and tilapia that the market can order?
Define variables and write an equation representing the relationship between the amount of each fish bought and how much the market spends.
Sketch a graph of the relationship. Label your axes.
[IMG]
On your graph, plot and label the combinations A—F.
|                   | A | B | C | D | E | F |
|-------------------|---|---|---|---|---|---|
| pounds of tilapia |   |   |   |   |   |   |
| pounds of salmon  |   |   |   |   |   |   |
Which of these combinations can the market order? Explain or show your reasoning.
List two ways you can tell if a pair of numbers is a solution to an equation.
Student Response
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Anticipated Misconceptions
If students let
\(x\)
be pounds of salmon, then the equation would be
\(5x + 3y = 210\)
and the coordinates would be reversed. The intercepts of the graph would be
\((0,70)\)
and
\((42,0)\)
. This is a good place to mention the importance of defining what quantities your variables represent.
Activity Synthesis
Ask students to share some strategies for graphing and features of their graphs. Invite 2–3 students to display their graphs. Consider asking:
"Was the slope of the line positive or negative? Why does that makes sense in this situation?" (In this relationship, as one quantity increases the other must decrease in order to keep the sum
\(3x + 5y\)
constant.)
"What was your strategy for graphing the relationship?" (Plotting points from question 1, using the table, figuring out the intercepts and connecting the line)
"Why does it make sense for the graph to be only in quadrant I?" (You cannot purchase a negative amount of fish, so the
\(x\)
and
\(y\)
values cannot be negative.)
"How is this situation different from the apples and oranges problem in a previous lesson?" (Buying
\(\frac12\)
pound of fish is reasonable while buying
\(\frac12\)
of an apple probably is not. )
Briefly reiterate key concepts: If a point is not on the graph of the equation then it is not a solution. The ordered pairs that are solutions to the equation all make the equation true and are all found on the line that is the graph of the equation.
A discussion could also include the detail that orders that are less than
$
210 can also be considered to work, because there is money left over. That gives an opportunity to discuss the shape of the graph of
\(3x + 5y \le 210\)
.


correct_option_index: 1