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.


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.


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.


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

5
options: Apply trigonometry to general triangles.

Understand similarity in terms of similarity transformations.

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

Understand congruence in terms of rigid motions.

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

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

Reason with shapes and their attributes.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Make geometric constructions.

Prove geometric theorems.

Find arc lengths and areas of sectors of circles.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Experiment with transformations in the plane.

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

Understand and apply the Pythagorean Theorem.

Explain volume formulas and use them to solve problems.

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

Apply geometric concepts in modeling situations.

Understand and apply theorems about circles.

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

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

Prove theorems involving similarity.

Analyze, compare, create, and compose shapes.
problem_activity: In Class Launch
Use after Unit 4, Lesson 9
Display an image of the flag of Nepal, such as this one, for all to see.
[IMG]
Tell students that this is the flag of Nepal, which is a country in South Asia that borders India and China. Ask students “What do you notice? What do you wonder?”
Students may notice:
It looks like it’s made of triangles.
I could break it up into a rectangle and three triangles.
The bottom left corner looks like a right angle.
Students may wonder:
What shapes is the flag made of?
Why does it look like this?
How could we break up the white symbols into simpler shapes?
If it does not come up during the discussion, ask students how they might break up the shape of the flag into simpler shapes so that they could, for example, find its area.
Then tell students that in this task they will see how to construct this flag, and investigate its shape. They will also investigate the shapes involved in a flag of their choosing.
Teacher Instructions
Students will not have seen how to trisect a line segment, which they will need to do in order to construct
\(AC\)
. They can measure first to see where the points that trisect the line should go. Instructions for trisecting a line segment can be found online. There are many ways of doing it, and some are easier than others, so if students find the instructions themselves they should be encouraged to compare several methods before deciding which one they prefer. If students try different methods, it could be beneficial to invite selected students to show the class what they did. The other steps for constructing the flag should be familiar. Having access to geometry software can streamline the construction process.
If students have trouble getting started with finding the angles, they can try giving
\(AB\)
a specific value and calculating the other side lengths.
Once students have completed the task, invite them to share the flags they chose and show how they adapted them to fit on the triangular banner.
Student-Facing Statement
The constitution of Nepal includes instructions for constructing the flag. Here are the instructions:
Step 1: Draw a line
\(AB\)
of the required length.
\(AB\)
will be the bottom edge of the flag.
Step 2: Draw a line
\(AC\)
perpendicular to
\(AB\)
so that the length of
\(AC\)
is
\(\frac43\)
the length of
\(AB\)
.
Step 3: Mark the point
\(D\)
on the line
\(AC\)
so that
\(AD\)
is the same length as
\(AB\)
. Then join the points
\(D\)
and
\(B\)
with a straight line.
Step 4: Mark the point
\(E\)
on the line
\(BD\)
so that
\(BE\)
is the same length as
\(AB\)
.
Step 5: Draw a line
\(FG\)
that goes through
\(E\)
, is parallel to
\(AB\)
, and is the same length as
\(AB\)
.
\(F\)
should be on the line
\(AC\)
.
Step 6: Join the points
\(C\)
and
\(G\)
with a straight line.
Construct the flag according to the instructions. You can make it any size you want.
Find the measure of each of the angles in the flag.
Imagine that there will be a parade featuring the flag of Nepal. For the parade there will be small flags and large flags. Decide what the sizes of each type of flag should be.
How much material would you need to make each type of flag?
If you made the border of the flags by sewing a ribbon along the edge, how long would the ribbon have to be for each type of flag?
Imagine that there will be a parade featuring a flag that is meaningful to you. (Choose a flag or design your own.) At the parade there will be small flags, large flags, and triangular banners like this:
[IMG]
How will you adapt your flag to fit on the triangular shape?
How much material of each color will you need for each kind of flag?
Teacher Instructions
Students who want an extra challenge can find the areas and perimeters of both the small and large flag in the second question, and then compare the areas to see the effect of the scale factor. The relationship between scaling lengths and scaling areas will be a topic in the next unit, so students do not need to have a full understanding of it at this time, but this is a good opportunity to preview the concept.
Another opportunity for an extra challenge is to try describing the exact ratios between the side lengths using radicals. An especially interesting thing students may notice is that the ratio between
\(AF\)
and
\(AD\)
is the same as the ratio between
\(AD\)
and
\(BD\)
,
\(\tfrac{1}{\sqrt2}\)
.
Having access to geometry software can help students visualize the shapes they are working with.
Once students have completed the task, invite them to share the flags they chose and show how they adapted them to fit on the triangular banner.
Student-Facing Statement
The constitution of Nepal includes instructions for constructing the flag. Here are the instructions:
Step 1: Draw a line
\(AB\)
of the required length.
\(AB\)
will be the bottom edge of the flag.
Step 2: Draw a line
\(AC\)
perpendicular to
\(AB\)
so that the length of
\(AC\)
is
\(\frac43\)
the length of
\(AB\)
.
Step 3: Mark the point
\(D\)
on the line
\(AC\)
so that
\(AD\)
is the same length as
\(AB\)
. Then join the points
\(D\)
and
\(B\)
with a straight line.
Step 4: Mark the point
\(E\)
on the line
\(BD\)
so that
\(BE\)
is the same length as
\(AB\)
.
Step 5: Draw a line
\(FG\)
that goes through
\(E\)
, is parallel to
\(AB\)
, and is the same length as
\(AB\)
.
\(F\)
should be on the line
\(AC\)
.
Step 6: Join the points
\(C\)
and
\(G\)
with a straight line.
Clare is constructing the flag and she starts with
\(AB\)
of length 6 inches. Here is her finished flag shape. Use the instructions to fill in as many lengths and angles as you can.
[IMG]
Imagine that there will be a parade featuring the flag of Nepal. For the parade there will be small flags and large flags. For one of those types, decide how big it should be.
How much material would you need to make the flag?
If you made the border of the flag by sewing a ribbon along the edge, how long would the ribbon have to be?
Imagine that there will be a parade featuring a flag that is meaningful to you. (Choose a flag or design your own.) At the parade there will be rectangular flags and triangular banners like this:
[IMG]
How will you adapt your flag to fit on the triangular shape?
How much material of each color will you need for each kind of flag?


correct_option_index: 15

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