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.


Your response:
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.


Your response:
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.


Your response:
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 that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Verify experimentally the properties of rotations, reflections, and translations:
- Lines are taken to lines, and line segments to line segments of the same length.
- Angles are taken to angles of the same measure.
- Parallel lines are taken to parallel lines.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
problem_activity: Activity
The purpose of this activity is for students to give precise descriptions of translations, rotations, and reflections. By the end of the previous lesson, students have identified and sketched these transformations from written directions, however they have not used this more precise language themselves to give descriptions of the three motions. The images in this activity are given on grids to allow and to encourage students to describe the transformation in terms of specific points, lines or angles. Describing the moves precisely and clearly will require students to engage in MP6.
There are four different transformation cards students use in this activity: 1A, 1B, 2A, and 2B. Each card has the original image and the image under a transformation. Students are arranged in groups of 2 and each one gets a different transformation card: some pairs are given cards 1A and 1B while other pairs get 2A and 2B. Each A card is a translation, while the B cards show either a rotation or reflection.
As students are describing their transformations and sketching their images under transformation, monitor for students using precise descriptions to their partner in terms of specific points, lines, or angles.
Digital
Launch
Introduce the word
transformation:
This is a word for a move (like the reflection in the warm-up) or for a sequence of moves. It's a mathematical word which will be used in place of "move," which has been used up to this point.
Arrange students in groups of 2. Display the original image that each student also has in front of them. Give each student one of the four transformation cards and tracing paper—make sure students know
not
to show their card to their partner! Tell students they will sketch a transformation based on directions given to them by a partner.
Partners have Cards 1A and 1B or Cards 2A and 2B. Tell students in the first round, those with the A cards give a precise description of the transformation displayed on their card to their partner. Their partners may use tracing paper to produce the image under transformation on the grid with the original image. In digital classrooms, students have access to applets they can use to transform the figure. When the sketch is complete, the student describing the transformation reveals their card, and together, students decide if the sketch is correct. In the second round, the roles are reversed. The students with the B cards describe their transformation while their partner sketches.
The student describing the transformation is allowed to repeat, revise, or add any important information as their partner sketches, however, they are not allowed to tell them to fix anything until they are finished. The student sketching should not speak, just sketch. (This is to encourage the describer to use mathematical language.) Remind students to use the geometric language for describing reflections, rotations, and translations that was used in the previous lesson.
Representation: Develop Language and Symbols.
Display or provide charts with symbols and meanings. For example, display the terms translation, rotation, and reflection and their respective meanings “slide,” “turn,” and “mirror,” accompanied by a visual example depicting the transformation. Remind students that they can refer to the display when giving directions to their partner.
Supports accessibility for: Conceptual processing; Memory
Listening, Speaking: Math Language Routine 2 Collect and Display.
This is the first time Math Language Routine 2 is suggested as a support in this course. In this routine, the teacher circulates and listens to student talk while jotting down words, phrases, drawings, or writing students use. The language collected is displayed visually for the whole class to use throughout the lesson and unit. Generally, the display contains different examples of students using features of the disciplinary language functions, such as interpreting, justifying, or comparing. The purpose of this routine is to capture a variety of students’ words and phrases in a display that students can refer to, build on, or make connections with during future discussions, and to increase students’ awareness of language used in mathematics conversations.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness
How It Happens:
As students describe the transformation of triangle
\(ABC\)
to their partner, listen for and collect vocabulary and phrases students use to describe the moves. Focus on capturing students using geometric language for describing reflections, rotations, and translations.
If the speaker is stuck, consider asking these questions: “How did point
\(A\)
transform to
\(A’\)
?”, “Choose one of the points, lines, or angles and describe how it changed.”, and “Overall, does it look like the new triangle is a translation, rotation, or reflection of the original?”
If using the applet, check for precision and labels as students place the new image under the transformation.
Write students’ words on a visual display. Divide the display into 3 sections. Group language about Cards 1A and 2A on the left side of the display, language about Card 1B in the middle, and language about Card 2B on the right side.
Record all language (whether precise, ambiguous, correct, or incorrect) in the appropriate column. as described by the students.
Arrange students in groups of 2, and invite partners to discuss which words or phrases stand out to them. Prompt students by asking, “Are there any words or phrases that stand out to you or don’t belong in a specific column? Why?” Again, circulate around the room, collecting any additional words, phrases, and sketches onto the display.
Students should notice that the left side consists of language describing translations, the middle consists of language describing reflections, and the right side consists of language describing rotations.
Select 3–4 groups to share their ideas with the class. Invite students to demonstrate their reasoning with the applet or tracing paper and be sure to modify the display accordingly.
Use this discussion to clarify, revise, and improve how ideas are communicated and represented. If students are still using vague words (e.g., move, flip, mirror image, etc.), reinforce the precise geometric terms (e.g., transformation, translation, rotation, reflection, etc.). Ask students, “Is there another way we can say this?” or “Can someone help clarify this language?”
Close this conversation by posting the display in the front of the classroom for students to reference for the remainder of the lesson, and be sure to update the display throughout the remainder of the lesson.
Student Facing
Your partner will describe the image of this triangle after a certain
transformation
. Sketch it here.
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
Introduce the word
transformation:
This is a word for a move (like the reflection in the warm-up) or for a sequence of moves. It's a mathematical word which will be used in place of "move," which has been used up to this point.
Arrange students in groups of 2. Display the original image that each student also has in front of them. Give each student one of the four transformation cards and tracing paper—make sure students know
not
to show their card to their partner! Tell students they will sketch a transformation based on directions given to them by a partner.
Partners have Cards 1A and 1B or Cards 2A and 2B. Tell students in the first round, those with the A cards give a precise description of the transformation displayed on their card to their partner. Their partners may use tracing paper to produce the image under transformation on the grid with the original image. In digital classrooms, students have access to applets they can use to transform the figure. When the sketch is complete, the student describing the transformation reveals their card, and together, students decide if the sketch is correct. In the second round, the roles are reversed. The students with the B cards describe their transformation while their partner sketches.
The student describing the transformation is allowed to repeat, revise, or add any important information as their partner sketches, however, they are not allowed to tell them to fix anything until they are finished. The student sketching should not speak, just sketch. (This is to encourage the describer to use mathematical language.) Remind students to use the geometric language for describing reflections, rotations, and translations that was used in the previous lesson.
Representation: Develop Language and Symbols.
Display or provide charts with symbols and meanings. For example, display the terms translation, rotation, and reflection and their respective meanings “slide,” “turn,” and “mirror,” accompanied by a visual example depicting the transformation. Remind students that they can refer to the display when giving directions to their partner.
Supports accessibility for: Conceptual processing; Memory
Listening, Speaking: Math Language Routine 2 Collect and Display.
This is the first time Math Language Routine 2 is suggested as a support in this course. In this routine, the teacher circulates and listens to student talk while jotting down words, phrases, drawings, or writing students use. The language collected is displayed visually for the whole class to use throughout the lesson and unit. Generally, the display contains different examples of students using features of the disciplinary language functions, such as interpreting, justifying, or comparing. The purpose of this routine is to capture a variety of students’ words and phrases in a display that students can refer to, build on, or make connections with during future discussions, and to increase students’ awareness of language used in mathematics conversations.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness
How It Happens:
As students describe the transformation of triangle
\(ABC\)
to their partner, listen for and collect vocabulary and phrases students use to describe the moves. Focus on capturing students using geometric language for describing reflections, rotations, and translations.
If the speaker is stuck, consider asking these questions: “How did point
\(A\)
transform to
\(A’\)
?”, “Choose one of the points, lines, or angles and describe how it changed.”, and “Overall, does it look like the new triangle is a translation, rotation, or reflection of the original?”
If using the applet, check for precision and labels as students place the new image under the transformation.
Write students’ words on a visual display. Divide the display into 3 sections. Group language about Cards 1A and 2A on the left side of the display, language about Card 1B in the middle, and language about Card 2B on the right side.
Record all language (whether precise, ambiguous, correct, or incorrect) in the appropriate column. as described by the students.
Arrange students in groups of 2, and invite partners to discuss which words or phrases stand out to them. Prompt students by asking, “Are there any words or phrases that stand out to you or don’t belong in a specific column? Why?” Again, circulate around the room, collecting any additional words, phrases, and sketches onto the display.
Students should notice that the left side consists of language describing translations, the middle consists of language describing reflections, and the right side consists of language describing rotations.
Select 3–4 groups to share their ideas with the class. Invite students to demonstrate their reasoning with the applet or tracing paper and be sure to modify the display accordingly.
Use this discussion to clarify, revise, and improve how ideas are communicated and represented. If students are still using vague words (e.g., move, flip, mirror image, etc.), reinforce the precise geometric terms (e.g., transformation, translation, rotation, reflection, etc.). Ask students, “Is there another way we can say this?” or “Can someone help clarify this language?”
Close this conversation by posting the display in the front of the classroom for students to reference for the remainder of the lesson, and be sure to update the display throughout the remainder of the lesson.
Student Facing
Your partner will describe the image of this triangle after a certain
transformation
. Sketch it here.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may get stuck thinking they need to use the precise terms for the transformation in their description. Encourage these students to describe it in a way that makes sense to them and to look for things they know about the specific points, lines, or angles on their card to help them.
Activity Synthesis
Display the following questions for all to see and give groups 2 minutes to discuss:
What pieces of your partner’s description were helpful when you were sketching?
What pieces did you find difficult to explain to your partner? Point to specific examples on your cards.
When you were sketching, what questions would have been helpful to be able to ask the describer?
Ask selected students who were observed using precise descriptions and sketching based on those descriptions to explain why they used the information they did and how it was helpful in sketching. Focus on:
The direction and distance of a translation.
The center and the measure of a rotation.
The line of a reflection.
If there is time, ask students who were both using and not using tracing paper to explain their process.
Reinforce the term
transformation
as a term that encompasses translations, rotations, and reflections. Tell them that there are other types of transformations, but for now, we will focus on these three types.


correct_option_index: 2