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: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Distinguish between situations that can be modeled with linear functions and with exponential functions.

For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
problem_activity: Activity
In this activity, students compare logarithmic expressions as they play a game of “war” in groups of 2. Students receive cards containing logarithms in bases 2, 5, and 10. The numbers in the expressions are written in all forms, including decimals, fractions, whole numbers, and exponential expressions. To compare the logarithms on the cards, they may:
determine if an expression is negative, zero, or positive, without finding the exact or estimated value
estimate the value of an expression such as
\(\log_2 10\)
by using logarithms with integer values
convert decimals to fractions to help find the logarithms
As students preview the deck by putting the cards in order from least to greatest, listen for how they decide on relative values of the cards. Students should not use calculators at this point.
Launch
Arrange students in groups of 2. The first 20 cards in the blackline master show log expressions with integer values. That last 10, which are labeled “challenge,” have non-integer values. Give each group only the first 20, the entire set of 30, or differentiate by giving some groups only the first 20 and some groups all of the cards.
Before students start playing, ask them to turn all the cards face up, and work with their partner to put them in order from least to greatest. The game will go more smoothly if students have a chance to gain familiarity with the contents of the card deck and evaluate each card in a lower-stakes interaction. This step may be skipped if students are comfortable determining the value of logarithmic expressions.
Speaking: MLR8 Discussion Supports.
To help students discuss the order of the cards with their partner, provide sentence frames such as: “I know _____ because . . .”, “Why did you . . . ?”, and “How do you know . . . ?”
Design Principle(s): Optimize output (for justification); Cultivate conversation
Engagement: Provide Access by Recruiting Interest.
Begin with a small-group or whole-class demonstration of how to play the game. Check for understanding by inviting students to rephrase directions in their own words. To scaffold the activity to allow for self-correction and multiple attempts, invite students to discard any cards that they may hesitate on into a separate, designated pile. Build in a few minutes for students to look through these cards after their first attempt. Then ask students to reshuffle and make a second attempt, noticing what strategies helped them to more quickly work through the more challenging cards.
Supports accessibility for: Memory; Conceptual processing
Student Facing
Have you played the game of war with a deck of playing cards?
Your teacher will give you and your partner a set of special cards.
Shuffle and deal the cards evenly.
Each player turns one card face up. The card with the greater value wins the round and its player captures both cards and sets them aside.
If you and your partner disagree about the value of a card, discuss until you reach an agreement.
If there is a tie, each player turns another card face up. The player whose card has the greater value captures all cards (including the cards that tie).
Play until all the cards are turned up. The player with the most cards wins.
Let the logarithm war begin!
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
Mai uses the fact that
\(\sqrt[3]{2}\)
is close to 1.25 and that
\(2^3=8\)
to make the estimate
\(\log_2(10) \approx 3\frac{1}{3}\)
. Explain Mai’s estimate. How exact is the estimate?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students may struggle making estimates to compare expressions. Ask them questions such as "Is the expression greater than or less than 0? How do you know? Is the expression greater than or less than 1? How do you know?" Make sure they understand that they only need to decide which is bigger; they do not need to calculate exact values.
Activity Synthesis
Much of the discussions will happen in groups, as students put the cards in order before playing the game and while playing the game. Invite groups to share any insightful or useful strategies for comparing any two cards that came up before or during the game.


correct_option_index: 2