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: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)
problem_activity: Activity
Students use a realistic food recipe to find equivalent ratios that represent different numbers of batches. Students use the original recipe to form ratios of ingredients that represent double, half, five times, and one-fifth of the recipe. Then they examine given ratios of ingredients and determine how many batches they represent.
Launch
Ask students if they have ever cooked something by following a recipe. If so, ask them what they made and what some of the ingredients were.
Ask: “How might we use ratios to describe the ingredients in your recipe?” (The ratios could associate the quantities of each ingredient being used.)
Explain to students that in this task, they will think about the ratios of ingredients for a tuna casserole and how to adjust them for making different numbers of batches.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills in problem solving, chunk this task into more manageable parts. For example, provide students with a task checklist which makes all the required components of the activity explicit.
Supports accessibility for: Memory; Organization
Listening: MLR8 Discussion Supports
. When asking the question, “How might we use ratios to describe the ingredients in your recipe?”, act out or use images that demonstrate the meaning of the terms "ratio", "recipe", and "ingredients" in the context of cooking. Demonstrate combining specific ingredients in their stated ratios. This will help students connect the language found in a recipe with the ratio reasoning needed for different batches of that recipe.
Design Principle(s): Support sense-making
Student Facing
Here is a recipe for tuna casserole.
Ingredients
3 cups cooked elbow-shaped pasta
6 ounce can tuna, drained
10 ounce can cream of chicken soup
1 cup shredded cheddar cheese
\(1 \frac12\)
cups French fried onions
[IMG]
Instructions
Combine the pasta, tuna, soup, and half of the cheese. Transfer into a 9 inch by 18 inch baking dish. Put the remaining cheese on top. Bake 30 minutes at 350 degrees. During the last 5 minutes, add the French fried onions. Let sit for 10 minutes before serving.
What is the ratio of the ounces of soup to the cups of shredded cheese to the cups of pasta in one batch of casserole?
How much of each of these 3 ingredients would be needed to make:
twice the amount of casserole?
half the amount of casserole?
five times the amount of casserole?
one-fifth the amount of casserole?
What is the ratio of cups of pasta to ounces of tuna in one batch of casserole?
How many batches of casserole would you make if you used the following amounts of ingredients?
9 cups of pasta and 18 ounces of tuna?
36 ounces of tuna and 18 cups of pasta?
1 cup of pasta and 2 ounces of tuna?
Student Response
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Student Facing
Are you ready for more?
The recipe says to use a 9 inch by 18 inch baking dish. Determine the length and width of a baking dish with the same height that could hold:
Twice the amount of casserole
Half the amount of casserole
Five times the amount of casserole
One-fifth the amount of casserole
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students who are not yet fluent in fraction multiplication from grade 5 may have difficulty understanding how to find half or one-fifth of the recipe ingredient amounts. Likewise, they may have difficulty identifying one-third of a batch. Suggest that they draw a picture of
\(\frac12\)
of 10, remind them that finding
\(\frac12\)
of a number is the same as dividing it by 2, or remind them that
\(\frac12\)
of a number means
\(\frac12\)
times that number.
Activity Synthesis
Display the recipe for all to see. Ask students to share and explain their responses. List their responses—along with the specified number of batches—for all to see. Ask students to analyze the list and describe how the ratio of quantities relate to the number of batches in each case. Draw out the idea that each quantity within the recipe was
multiplied
by a number to obtain each batch size, and that each ingredient amount is multiplied by the
same
value.
In finding one-half and one-fifth of a batch, students may speak in terms of dividing by 2 and dividing by 5. Point out that “dividing by 2” has the same outcome as “multiplying by one-half,” and “dividing by 5” has the same outcome as “multiplying by one-fifth.” (Students multiplied a whole number by a fraction in grade 5.) Later, we will want to state our general definition of equivalent ratios as simply as possible: as
multiplying
both
\(a\)
and
\(b\)
in the ratio
\(a:b\)
by the same number (not “multiplying or dividing”).


correct_option_index: 1