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: Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Measure lengths indirectly and by iterating length units.

Represent and interpret data.

Classify objects and count the number of objects in each category.

Relate addition and subtraction to length.

Tell and write time.

Describe and compare measurable attributes.

Work with time and money.

Measure and estimate lengths in standard units.

Convert like measurement units within a given measurement system.

Geometric measurement: understand concepts of angle and measure angles.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
problem_activity: Narrative
The purpose of this activity is for students to convert between measurements in milliliters and liters, providing practice multiplying and dividing by 1,000. Students work with numbers in many forms including whole numbers, decimals, fractions, and numbers in exponential form.
Engagement: Internalize Self-Regulation.
Synthesis: Provide students an opportunity to self-assess and reflect on their own progress. For example, provide students with a partially completed chart to compare their answers and talk about the similarities and differences with their partners.
Supports accessibility for: Attention; Memory; Social-Emotional Functioning
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?” (There are different sized water bottles. There are numbers underneath the water bottles. How much more water does the big one hold than the little one? How many milliliters are in a liter?)
Display a table like this one:
|  L  |   mL    |
|-----|---------|
|  1  |  1,000  |
| 10  |         |
| 0.1 |         |
|     | 100,000 |
|     |   10    |
“What numbers go in the empty boxes in the table?”
30 seconds quiet think time
“Explain your thinking to a partner.”
Fill in the table and leave it displayed for students to refer to during the lesson.
|  L   |   mL    |
|------|---------|
|  1   |  1,000  |
|  10  | 10,000  |
| 0.1  |   100   |
| 100  | 100,000 |
| 0.01 |   10    |
Activity
3–5 minutes: independent work time
1–2 minutes: partner discussion
Monitor for students who:
compare the quantities by converting milliliters to liters
compare by converting liters to milliliters
Student Facing
[IMG]
Complete the table.
|    L     |    mL    |
|----------|----------|
|    5     |          |
|   6.3    |          |
|   0.95   |          |
| \(10^2\) |          |
|          | 800,000  |
|          | \(10^6\) |
|          |    65    |
Decide if the two measurements are equal. If not, choose which one is greater. Explain or show your reasoning.
15 mL and 0.15 L
2,500 mL and 2.5 L
200 mL and
\(\frac{1}{4}\)
L
1 mL and
\(\frac{1}{1,000}\)
L
15,600 mL and 15.5 L
Student Response
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Advancing Student Thinking
If students confuse the operations they need to use to convert milliliters to liters or liters to milliliters, refer to the table from the launch and ask, “What patterns do you notice?”
If necessary, add rows to the table and ask them to explain how many milliliters of water are in 2 liters of water and 3 liters of water, and 0.001 liter of water.
Activity Synthesis
Invite selected students to share how they compared the measurements.
Display: 15,600 mL and 15.5 L
“How many liters are 15,600 milliliters? How do you know?” (15.6 since I divide by 1,000)
“How many milliliters are 15.5 liters? How do you know?” (15,500 since there are 1,000 milliliters in each liter so that’s 15,000 and half of a thousand which is 500.)
“Which is greater? 15,600 milliliters or 15.5 liters? How do you know?” (15,600 mL because I can compare them using either liters or milliliters.)
“When you solved this problem, did you convert from milliliters to liters or from liters to milliliters? Why?” (I converted from liters to milliliters because multiplying by 1,000 is more comfortable than dividing by 1,000.)


correct_option_index: 10