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.


Your response:
{
  "explanation": "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.


Your response:
{
  "explanation": "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.


Your response:
{
  "explanation": "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: Analyze and solve pairs of simultaneous linear equations.

Solve linear equations in one variable.
problem_activity: Activity
In the previous activity, the system of equations was represented in words, a table, and a graph. In this activity, the system of equations is partially given in words, but key elements are only provided in the graph. Students have worked with lines that represent a context before. Now they must work with two lines at the same time to determine whether a point lies on one line, both lines, or neither line.
Teacher Notes for IM 6–8 Math Accelerated
This activity is optional. Use this activity if time allows to preview some of the work ahead with systems of equations or if students need additional practice making connections between points on and off graphed lines as they relate to a context. Due to the sequence of IM 6–8 Math Accelerated, this activity is in a different lesson so the reference to the “previous activity” in the narrative should be disregarded.
Launch
Arrange students in groups of 2. Give students 1 minute to read the problem and answer any questions they have about the context. Tell students to complete the table one row at a time with one person responding for Clare and the other responding for Andre. Give students 2–3 minutes to finish the table followed by whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts for students who benefit from support with organizational skills in problem solving. Check in with students within the first 2–3 minutes of work time to ensure that they have understood the directions. If students are unsure how to begin, suggest that they consider each statement for Clare first, and then for Andre.
Supports accessibility for: Organization; Attention
Writing, Speaking: MLR5 Co-Craft Questions.
Display the graph that shows Clare and Andre’s progress of making signs, without showing the table. Ask students to write down possible mathematical questions that can be asked about the situation, and then share with a partner. As students discuss, listen for and amplify questions that notice and wonder about the points A, B, C, and D; the location of these points; and why the points were possibly highlighted and what it means in context of the situation. Finally, reveal the table from the activity or use questions generated by the students and allow time to work on them. This will help students make sense of a graph with two lines at the same time by generating questions using mathematical language.
Design Principle(s): Cultivate conversation; Maximize meta-awareness
Student Facing
Clare and Andre are making signs for all the lockers as part of the decorations for the upcoming spirit week. Yesterday, Andre made 15 signs and Clare made 5 signs. Today, they need to make more signs. Each person's progress today is shown in the coordinate plane.
[IMG]
Based on the lines, mark the statements as true or false for each person.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "width:60px"}, "_value": "point"}, {"_attributes": {"scope": "col", "style": "width:230px"}, "_value": "what it says"}, {"_attributes": {"scope": "col", "style": "width:80px"}, "_value": "Clare"}, {"_attributes": {"scope": "col", "style": "width:80px"}, "_value": "Andre"}]}]}], "tbody": [{"tr": [{"td": [{"_attributes": {"style": "width:60px"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "2"}, "_value": "\\(A\\)"}]}, {"_attributes": {"style": "width:230px"}, "_value": "At 40 minutes, I have 25 signs completed."}, {"_attributes": {"style": "width:80px"}}, {"_attributes": {"style": "width:80px"}}]}, {"td": [{"_attributes": {"style": "width:60px"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "6"}, "_value": "\\(B\\)"}]}, {"_attributes": {"style": "width:230px"}, "_value": "At 75 minutes, I have 42 and a half signs completed."}, {"_attributes": {"style": "width:80px"}}, {"_attributes": {"style": "width:80px"}}]}, {"td": [{"_attributes": {"style": "width:60px"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "7"}, "_value": "\\(C\\)"}]}, {"_attributes": {"style": "width:230px"}, "_value": "At 0 minutes, I have 15 signs completed."}, {"_attributes": {"style": "width:80px"}}, {"_attributes": {"style": "width:80px"}}]}, {"td": [{"_attributes": {"style": "width:60px"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "12"}, "_value": "\\(D\\)"}]}, {"_attributes": {"style": "width:230px"}, "_value": "At 100 minutes, I have 60 signs completed."}, {"_attributes": {"style": "width:80px"}}, {"_attributes": {"style": "width:80px"}}]}]}]}]}
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
4 toothpicks make 1 square
7 toothpicks make 2 squares
10 toothpicks make 3 squares
[IMG]
Do you see a pattern? If so, how many toothpicks would you need to make 10 squares according to your pattern? Can you represent your pattern with an expression?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Display the graphs from the task statement. The goal of this discussion is for students to realize that points that lie on one line can be interpreted as statements that are true for Clare, and points that lie on the other line as statements that are true for Andre. Ask students:
“What is true for Clare and Andre after 20 minutes?” (Clare has 15 signs completed and Andre has 20 signs completed.)
“What, then, do you know about the point
\((20, 15)\)
and the equation for Clare's graph?” (The point
\((20, 15)\)
is a solution to the equation for Clare's graph.)
“What do you know about the point
\((20, 20)\)
and the equation for Andre's graph?” (The point
\((20, 20)\)
is a solution to the equation for Andre's graph.)
Invite groups to share their reasoning about points A–D. Conclude by pointing out to students that, in this context, there are many points true for Clare and many points true for Andre but only one point true for both of them. Future lessons will be about how to figure out that point.


correct_option_index: 0