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

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fl_problem_000674

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options: Apply trigonometry to general triangles.

Prove geometric theorems.

Explain volume formulas and use them to solve problems.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Understand and apply the Pythagorean Theorem.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Translate between the geometric description and the equation for a conic section.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Prove theorems involving similarity.

Define trigonometric ratios and solve problems involving right triangles.

Solve real-world and mathematical problems involving area, surface area, and volume.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Make geometric constructions.

Use coordinates to prove simple geometric theorems algebraically.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Find arc lengths and areas of sectors of circles.

Experiment with transformations in the plane.

Classify two-dimensional figures into categories based on their properties.

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

Understand similarity in terms of similarity transformations.

Reason with shapes and their attributes.

Visualize relationships between two-dimensional and three-dimensional objects.

Analyze, compare, create, and compose shapes.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Understand and apply theorems about circles.
problem_activity: Activity
In this activity, students get another opportunity to practice drawing dilations precisely. They also get to see the effects of different scale factors on an image. By assigning students scale factors less than and greater than one, students get a chance to see how the image is taken closer to or farther away from the center of dilation. By assigning equivalent scale factors, such as
\(\frac32\)
and 1.5, students get a chance to explore how images dilated with the same scale factor are congruent. They also get a chance to remind themselves of decimal representations of fractions, which will be useful when they calculate scale factors from ratios of side lengths in later lessons.
Launch
Arrange students in groups of 2. Assign each student a scale factor from the list:
\(\frac14\)
,
\(\frac12\)
,
\(\frac34\)
,
\(\frac76\)
,
\(\frac32\)
,
\(\frac52\)
, 0.25, 0.5, 1.5, 2.5
Representation: Internalize Comprehension.
Chunk this task into more manageable parts to differentiate the degree of difficulty or complexity. Assign
\(\frac12\)
and
\(\frac32\)
to a pair of students who would benefit from additional support.
Supports accessibility for: Conceptual processing; Organization; Attention
Student Facing
Here is a center of dilation and a triangle.
[IMG]
Measure the sides of triangle
\(EFG\)
(to the nearest mm).
Your teacher will assign you a scale factor. Predict the relative lengths of the original figure and the image after you dilate by your scale factor.
Dilate triangle
\(EFG\)
using center
\(C\)
and your scale factor.
How does your prediction compare to the image you drew?
Use tracing paper to copy point
\(C\)
, triangle
\(EFG\)
, and your dilation. Label your tracing paper with your scale factor.
Align your tracing paper with your partner’s. What do you notice?
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?
[IMG]
Dilate triangle
\(FEG\)
using center
\(C\)
and scale factors:
\(\frac12\)
2
What scale factors would cause some part of triangle
\(E'F'G'\)
’ to intersect some part of triangle
\(EFG\)
?
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
If students are unclear about relative lengths, tell them to make a prediction and write a description such as “a little smaller” or “a lot bigger” before they calculate.
Activity Synthesis
The goal of this discussion is to identify the effects of various scale factors. Collect and align several tracing papers on the original image. Invite students to make generalizations about different scenarios:
compare scale factors which are greater and less than one
compare equivalent scale factors with different representations (such as 0.5 and
\(\frac12\)
)
Speaking: MLR8 Discussion Supports.
Use this routine to help students produce statements about the scale factor of a dilation. Provide sentence frames for students to use when they generalize the effects of various scale factors, such as: “If _____ , then _____ because….” and “_____ will always _____ because….”
Design Principle(s): Support sense-making; Optimize output (for generalization)


correct_option_index: 16