few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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.
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fl_problem_000674

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options: Prove that all circles are similar.

Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Construct a tangent line from a point outside a given circle to the circle.

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
problem_activity: In Class Launch
Use after Unit 3, Lesson 11
In this task, students will experiment with cups in order to see what shape they seem to trace out when they are rolled on a flat surface, and then refine their thinking in order to prove what the shape is. If possible, provide cups with a variety of sizes and shapes. Note that cylindrical cups will not curve as they are rolled, and so will not make the same kind of shape as cups with slanted sides.
Ask students to roll some cups around. Then ask them to guess what shape the cup traces out on the table or floor. Sketch the suggested shapes for all to see. Tell students their task is to try to prove what the shape is.
Teacher Instructions
Consider the types of cups to make available to students and how they will be able to manipulate the cups. For example, paper cups can be cut apart and unrolled, but plastic cups can’t. If materials are limited and need to be reused in multiple class periods, consider providing an intact cup and a cup that has already been cut apart so that students can examine both of them.
After students have completed the task, either invite them to share how they knew what shape the cup would trace out, or have a gallery walk so that students can see and comment on each other’s arguments.
Then invite them to share their responses to the last question: how did they make a cup that would trace out the largest possible area? If no student mentions it, ask what would happen if the sides of the cup weren’t slanted at all. (In theory, the cup will roll forever and trace out an infinite area, but in reality, it will run into something eventually and stop.)
Technology can be helpful when students are experimenting with different possible cup shapes. If technology is available, here is an applet students can use:
Student-Facing Statement
What shape does a cup trace out when it is rolled on a flat surface? Use words and pictures to explain how you know.
How can you locate the center and calculate the area of the shape that is traced out?
Using one sheet of 8.5 inch by 11 inch paper, how could you make a cup that will trace out the largest possible area?
Teacher Instructions
Consider the types of cups to make available to students and how they will be able to manipulate the cups. For example, paper cups can be cut apart and unrolled, but plastic cups can’t. If materials are limited and need to be reused in multiple class periods, consider providing an intact cup and a cup that has already been cut apart so that students can examine both of them.
If students see the questions in Part 2 before they have finished Part 1, it will give away the shape that the cup traces out, so hand out Part 2 after the discussion of Part 1. Part 1 can be discussed before all students have finished their explanations, as long as they all have some developed ideas about what the shape is. For the discussion, ask students to share what shape they think the cup traces out and why they think so. Students do not need to have fully developed proofs, but take the opportunity to press them to clarify their terminology and justify their assumptions.
After students have completed the task, invite them to share their responses to the last question: how did they make a cup that would trace out a larger area? (The bottom radius should be closer to the top radius so that the radius of the ring will be larger, or the cup should be taller so that the ring is thicker.) Then ask how they would make a shape that traces out the largest possible area. If no student mentions it, ask what would happen if the sides of the cup weren’t slanted at all. (In theory, the cup will roll forever and trace out an infinite area, but in reality, it will run into something eventually and stop.)
Technology can be helpful when students are experimenting with different possible cup shapes. If technology is available, here is an applet students can use:
Student-Facing Statement
Part 1:
What shape does a cup trace out when it is rolled on a flat surface? Explain or show your reasoning.
Pause for discussion.
Part 2:
The outside of this ring has a radius of 55 cm. The inside of the ring has a radius of 38 cm. Find the area of the ring.
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Triangle
\(ABC\)
is isosceles. Find the length of side
\(AC\)
using the information given. The two vertical lines are parallel.
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Here is the cross-section of a cup. It shows the width of the cup at the top and at the bottom, and the slant height of the cup. If we extend the sides of the cup down until they meet at a point, we will make a triangle. What would the slant height of that triangle be?
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Measure the widths of the top and bottom of your cup, and measure its slant height. If you drew the cross-section of the cup and then extended the sides to make a triangle, what would the slant height of the triangle be?
If you rolled your cup in a circle to make a ring, what would the area of the ring be?
Give an example of a cup that would trace out a larger area than your cup would.


correct_option_index: 0

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