few_shots: 
Example 1:
Concept/skill: 
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.

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.


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

Example 2:
Concept/skill: 
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.

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} $

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Example 3:
Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

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?


Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_neg_0

5
standard_description: Solve linear equations in one variable.
problem_activity: Activity
The purpose of this activity is to give students practice finding missing side lengths in a right triangle using the Pythagorean Theorem.
Teacher Notes for IM 6–8 Math Accelerated
Adjust time to 15 minutes. After 2–3 minutes of work time, select 1–2 groups to share their work for the first question before continuing with the remaining questions. If time is limited, tell students that the final question is optional.
Launch
Arrange students in groups of 2. Give students 10 minutes of quiet work time and then have them compare with a partner. If partners disagree about any of their answers, ask them to explain their reasoning to one another until they reach agreement. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge by displaying the Pythagorean Theorem with a labeled diagram. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
Find
\(c\)
.
[IMG]
Find
\(b\)
.
[IMG]
A right triangle has sides of length 2.4 cm and 6.5 cm. What is the length of the hypotenuse?
A right triangle has a side of length
\(\frac14\)
and a hypotenuse of length
\(\frac13\)
. What is the length of the other side?
Find the value of
\(x\)
in the figure.
[IMG]
Student Response
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click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
The spiral in the figure is made by starting with a right triangle with both legs measuring one unit each. Then a second right triangle is built with one leg measuring one unit, and the other leg being the hypotenuse of the first triangle. A third right triangle is built on the second triangle’s hypotenuse, again with the other leg measuring one unit, and so on.
[IMG]
Find the length,
\(x\)
, of the hypotenuse of the last triangle constructed in the figure.
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
Ask students to share how they found the missing side lengths. If students drew triangles for the two questions that did not have an image, display a few of these for all to see, noting any differences between them. For example, students may have drawn triangles with different orientations or labeled different sides as
\(a\)
and
\(b\)
.
For the last question, ask students to say what they did first to try and solve for
\(x\)
. For example, while many students may have found the length of the unknown altitude first and then used that value to find
\(x\)
, others may have set up the equation
\(34-5^2=18-x^2\)
.
Point out that when you know two sides of a right triangle, you can always find the third by using the Pythagorean identity
\(a^2 + b^2 = c^2\)
. Remind them that it is important to keep track of which side is the hypotenuse.
Reading, Writing, Speaking: MLR3 Clarify, Critique, Correct.
Before students share their method for the questions that did not have an image, present an incorrect solution based on a common error related to labeling the sides of a right triangle. For the right triangle with a side of length
\(\frac{1}{4}\)
and a hypotenuse of length
\(\frac{1}{3}\)
, draw a right triangle with the legs labeled
\(\frac{1}{4}\)
and
\(\frac{1}{3}\)
. Provide an incorrect explanation such as: “I know that
\(a = \frac{1}{4}\)
and
\(b = \frac{1}{3}\)
, so when I use the Pythagorean Theorem, I get the equation
\((\frac{1}{4})^2 + (\frac{1}{3})^2 = c^2\)
.” Ask students to identify the error, critique the reasoning, and revise the original statement. As students discuss in partners, listen for students who clarify the meaning of the hypotenuse and identify
\(c\)
as the length of the hypotenuse in the Pythagorean Theorem. This routine will engage students in meta-awareness as they critique and correct a common error when labeling the sides of a right triangle.
Design Principles(s): Cultivate conversation; Maximize meta-awareness


aligns: no