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

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: Activity
In this task, students practice finding unit prices, using different reasoning strategies, and articulating their reasoning. They also learn about the term “at this rate.”
As students work, observe their work and then assign one problem for each group to own and present to the class. (The problems can each be assigned to more than one group). Have them work together to create a visual display of their problem and its solution.
Teacher Notes for IM 6–8 Accelerated
Adjust this activity to 10 minutes.
In the launch, adjust the displayed problem to: “Pizza costs
$
10 for 8 slices. At this rate, how much will 6 slices cost?” During the discussion of the phrase “at this rate,” ask students to outline a method for solving the problem. Highlight any methods that determine the cost for 1 slice of pizza. Tell students that the price for 1 item is called the
unit price
and can be described using the word “per.” For example, “This pizza costs
$
1.25 per slice.”
Tell students to omit the last question in which they create a visual display.
Digital
Launch
Arrange students in groups of 3–4. Provide tools for creating a visual display and access to rulers. Explain that they will work together to solve some shopping problems, run their work by you, and prepare to present an assigned problem to the class. Tell students that they can use double number lines if they wish.
Display the problem and read it aloud: Pizza costs
$
1.25 per slice. At this rate, how much will 6 slices cost?
Ask students what they think “at this rate” means in the question. Ensure they understand that “at this rate” means we know that equivalent ratios are involved:
The ratio of cost to number of slices is
$
1.25 to 1. That is, pizza costs
$
1.25 per slice.
The ratio of cost to number of slices is
something
to 6. That is, pizza costs
something
for 6 slices.
The
something
is the thing we are trying to figure out, and “at this rate” tells us that the two ratios in this situation are equivalent. Another way to understand “at this rate” in this context is “at this price per unit” and that the price per unit is the same no matter how many items or units are purchased.
Discuss any expectations for the group presentation. For example, each group member might be assigned a specific role for the presentation.
If students have digital access, they can use an applet to explore the problems and justify their reasoning before preparing their presentations.
Student Facing
Four bags of chips cost
$
6.
What is the cost per bag?
At this rate, how much will 7 bags of chips cost?
At a used book sale, 5 books cost
$
15.
What is the cost per book?
At this rate, how many books can you buy for
$
21?
Neon bracelets cost
$
1 for 4.
What is the cost per bracelet?
At this rate, how much will 11 neon bracelets cost?
Pause here so your teacher can review your work.
Your teacher will assign you one of the problems. Create a visual display that shows your solution to the problem. Be prepared to share your solution with the class.
Here is an applet you may use if you choose to.
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
Arrange students in groups of 3–4. Provide tools for creating a visual display and access to rulers. Explain that they will work together to solve some shopping problems, run their work by you, and prepare to present an assigned problem to the class. Tell students that they can use double number lines if they wish.
Display the problem and read it aloud: Pizza costs
$
1.25 per slice. At this rate, how much will 6 slices cost?
Ask students what they think “at this rate” means in the question. Ensure they understand that “at this rate” means we know that equivalent ratios are involved:
The ratio of cost to number of slices is
$
1.25 to 1. That is, pizza costs
$
1.25 per slice.
The ratio of cost to number of slices is
something
to 6. That is, pizza costs
something
for 6 slices.
The
something
is the thing we are trying to figure out, and “at this rate” tells us that the two ratios in this situation are equivalent. Another way to understand “at this rate” in this context is “at this price per unit” and that the price per unit is the same no matter how many items or units are purchased.
Discuss any expectations for the group presentation. For example, each group member might be assigned a specific role for the presentation.
If students have digital access, they can use an applet to explore the problems and justify their reasoning before preparing their presentations.
Student Facing
Four bags of chips cost
$
6.
What is the cost per bag?
At this rate, how much will 7 bags of chips cost?
At a used book sale, 5 books cost
$
15.
What is the cost per book?
At this rate, how many books can you buy for
$
21?
Neon bracelets cost
$
1 for 4.
What is the cost per bracelet?
At this rate, how much will 11 neon bracelets cost?
Pause here so your teacher can review your work.
[IMG]
Your teacher will assign you one of the problems. Create a visual display that shows your solution to the problem. Be prepared to share your solution with the class.
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
The first and third questions involve using decimals to represent cents. If the decimal point is forgotten, remind students that the cost of the bracelet is less than one dollar, and the cost of the chips is in between one and two dollars.
Watch for students working in cents instead of dollars for the bracelets. They may come up with an answer of 275 cents. For these students, writing 25 cents as \$0.25 should help, or consider reminding them of the avocados from a previous activity, which had a unit price of \$0.50.
Activity Synthesis
Invite each group to present its assigned problem. After each group presents, highlight the group’s strategy, accurate uses of the terms “at this rate” and “per,” and the ways in which a double number line might have been used when working with unit price.


correct_option_index: 0