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.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response:
Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

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} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

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?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response:
Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Understand ratio concepts and use ratio reasoning to solve problems.

Analyze proportional relationships and use them to solve real-world and mathematical problems.
problem_activity: Optional activity
The purpose of this activity is to provide a context where a ratio of fractions arises naturally, and students need to find an equivalent ratio to solve the problem. The ratio
\(2 \frac12: 1 \frac34\)
is equivalent to
\(10:7\)
, so a scaled copy of the Mona Lisa that is 10 inches by 7 inches would fit on the cover of the notebook. Other answers are possible. Some students might try to find the biggest possible copy that will fit on the cover, which would result in a different scale factor.
The digital version of the student materials includes an applet so that students can experiment with the context, because there are many related measurements within the context that can be hard to visualize. For example, the applet makes it clear that you can't simply scale down the Mona Lisa and make it perfectly fit on the notebook, since the notebook and the Mona Lisa are not scaled copies of each other. It also serves to remind students that the length and width of the Mona Lisa have to be scaled by the same factor, or the image becomes distorted.
Students discuss how they found their solution with a partner and determine if the scale factors they came up with are reasonable. Students must think about whether it makes sense to try to scale the picture so that it fills as much of the page as possible, or whether it makes more sense to leave room for a title. As students discuss with their partner, identify pairs of students who have a good argument that a certain scale factor makes more sense to use than another. Ask these students to share during the whole class discussion.
Digital
Launch
If desired, show students an image of the Mona Lisa.
If using the print version, and appropriate technology is available, consider displaying the applet for everyone to see to help students better understand the situation
ggbm.at/j8B9vZKV
.
The purpose of the applet is for experimenting and understanding the situation. If using it, demonstrate how it works, and ask students to think about:
How to use the applet to create scale copies of the Mona Lisa (both dimensions have to be adjusted by the same factor.)
Is it possible to scale down the Mona Lisa so that it perfectly covers the notebook? (No, choices have to be made about what the final product will look like.)
Arrange students in groups of 2. Give 3–5 minutes of quiet work time to do the problem. Then, ask them to take turns sharing with their partner the method used to calculate scale factor and reasonableness of their answers.
If using the digital activity, still have students work in groups of 2 and have them work individually on the problem with the applet, before sharing their method(s) to calculate scale factor with their partner.
Conversing, Representing, Writing: MLR2 Collect and Display.
As students discuss the scale factor they used, listen for and collect mathematical language students use to describe the strategies they used to find scale factors. Throughout the remainder of the lesson, continue to update collected student language and remind students to borrow language from the display as needed. This will help students use mathematical language during paired and group discussions.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness
Student Facing
In real life, the Mona Lisa measures
\(2 \frac12\)
feet by
\(1 \frac34\)
feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.
The applet is here to help you experiment with the situation. (It won't solve the problems for you.) Use the sliders to scale the image and drag the red circle to place it on the book. Measure the side lengths with the Distance or Length tool.
What size should they use for the scaled copy of the Mona Lisa on the notebook cover?
What is the scale factor from the real painting to its copy on the notebook cover?
Discuss your thinking with your partner. Did you use the same scale factor? If not, is one more reasonable than the other?
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
If desired, show students an image of the Mona Lisa.
If using the print version, and appropriate technology is available, consider displaying the applet for everyone to see to help students better understand the situation
https://ggbm.at/j8B9vZKV
.
The purpose of the applet is for experimenting and understanding the situation. If using it, demonstrate how it works, and ask students to think about:
How to use the applet to create scale copies of the Mona Lisa. (Both dimensions have to be adjusted by the same factor.)
Is it possible to scale down the Mona Lisa so that it perfectly covers the notebook? (No, choices have to be made about what the final product will look like.)
Arrange students in groups of 2. Give 3–5 minutes of quiet work time to do the problem. Then, ask them to take turns sharing with their partner the method used to calculate scale factor and reasonableness of their answers.
If using the digital activity, still have students work in groups of 2 and have them work individually on the problem with the applet, before sharing their method(s) to calculate scale factor with their partner.
Conversing, Representing, Writing: MLR2 Collect and Display.
As students discuss the scale factor they used, listen for and collect mathematical language students use to describe the strategies they used to find scale factors. Throughout the remainder of the lesson, continue to update collected student language and remind students to borrow language from the display as needed. This will help students use mathematical language during paired and group discussions.
Design Principle(s): Optimize output (for explanation); Maximize meta-awareness
Student Facing
In real life, the Mona Lisa measures
\(2 \frac12\)
feet by
\(1 \frac34\)
feet. A company that makes office supplies wants to print a scaled copy of the Mona Lisa on the cover of a notebook that measures 11 inches by 9 inches.
What size should they use for the scaled copy of the Mona Lisa on the notebook cover?
What is the scale factor from the real painting to its copy on the notebook cover?
Discuss your thinking with your partner. Did you use the same scale factor? If not, is one more reasonable than the other?
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 might get stuck thinking the scaled copy needs to measure 11 inches by 9 inches.  Ask students:
Does the copy of the painting have to cover the entire notebook?
What are some other options if the image doesn't cover the entire notebook?
What if the image is bigger than the notebook cover? What if it is smaller?
Activity Synthesis
Select previously identified students to share the arguments they had with their partners.  Some guiding questions:
What scale factor did you and your partner agree upon? How did you both agree upon this?
Were there any similarities between the methods you and your partner used?  Were there any differences?


correct_option_index: 1