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.


Standard options: 
A. Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.
Answer: B

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?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
problem_activity: Narrative
This activity prompts students to examine patterns in multiples of 10 and 9, and to notice that the digits in the multiples of 9 can be reasoned in relation to the more-familiar multiples of 10. Students use what they know about the place value and operations to explain the patterns in these multiples (MP7). For instance, students may reason that, because 9 is 1 less than 10, to find
\(12 \times 9\)
is to find the
\(12 \times 10\)
and then subtract 1 twelve times (or subtract
\(12 \times 1\)
) from the product.
The reasoning in this activity prepares them to notice patterns in the multiples of 100 and 99 in the next lesson.
MLR8 Discussion Supports.
Use multimodal examples to show the patterns of both columns. Use verbal descriptions along with gestures, drawings, or concrete objects to show the connection between the multiples of 9 and 10.
Advances: Listening, Representing
Representation: Access for Perception.
Synthesis: Use pictures of the long rectangle base-ten blocks to help students visualize the patterns. For example, display a picture of eight long rectangle base-ten blocks. Count by 10 while pointing to each block. Then, cross out one unit in each block and discuss how this shows that counting by 9 is like multiplying by 10 and subtracting.
Supports accessibility for: Conceptual Processing, Visual Spatial Processing
Launch
Groups of 2
Read the opening paragraph as a class.
“Which do you prefer, counting by 10 or counting by 9? Why?” (Counting by 10 because I've been doing that since kindergarten.)
30 seconds: partner discussion
“Let’s look at numbers we get by counting by 9 and by 10 and see what patterns we can find.”
Activity
“Take a few quiet minutes to work on the first few problems. Then, share your thinking and complete the rest of the activity with your partner.”
5–6 minutes: independent work time
5–6 minutes: partner discussion
Monitor for students who:
can clearly explain the pattern of the digits in multiples of 10 in terms of place value
notice connections between the values in the two columns and use them to explain the patterns in the digits in multiples of 9
Student Facing
Andre’s class is choral counting by 10 and then by 9. The left column shows the numbers they say when counting by 10.
Complete the right column with the first ten numbers the class will say when counting by 9.
What patterns do you notice about the features of the numerical patterns? Make at least two observations about each list of numbers.
| counting by 10 | counting by 9 |
|----------------|---------------|
|       10       |               |
|       20       |               |
|       30       |               |
|       40       |               |
|       50       |               |
|       60       |               |
|       70       |               |
|       80       |               |
|       90       |               |
|      100       |               |
For the numbers in the “counting by 10” column, why do you think:
the digits in the tens place change the way they do?
the digits in the ones place are the way they are?
For the numbers in the “counting by 9” column, why do you think the digits in the ones place change the way they do? Explain your reasoning.
Student Response
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Advancing Student Thinking
Students may not see that the digit in the ones place decreases by 1 each time the count goes up by 9. Consider asking:
“What patterns do you see in the pair of numbers in each row?”
“How do you think the numbers in the ‘counting by 9’ column are related to those in the ‘counting by 10’ column?”
Activity Synthesis
Display the completed table.
Invite students to share the patterns they noticed in the numbers in each column. Record their observations by annotating the numbers in the table.
If no students mentioned that the two sets of numbers are multiples of 10 and multiples of 9, ask them about it.
Select previously identified students to share their responses to the last two problems.
If no students reason that counting by 9 can be thought of as counting by 10 and subtracting 1 each time, bring this to their attention.
In other words, counting by 9 once means
\(10- 1\)
, which is 9. Counting by 9 again means adding another
\(10 -1\)
to 9, or
\(9 + 10 - 1\)
, which is 18.  Counting by 9 a third time means
\(18 + 10 - 1\)
, which is 27. And so on.
“Counting by 9 eight times is the same as counting by 10 eight times and subtracting 1 eight times, or
\((8 \times 10) - (8 \times 1)\)
, which is
\(80 - 8\)
or 72.”


correct_option_index: 0