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 multiply multi-digit whole numbers using the standard algorithm.

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: 
Yes. 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.

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_pos_0

5
standard_description: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
problem_activity: Optional activity
This activity gives students a chance to apply what they know about scale factors, lengths, and angles and create scaled copies without the support of a grid. Students work in groups of 3 to complete a jigsaw puzzle, each group member scaling 2 non-adjacent pieces of a 6-piece puzzle with a scale factor of
\(\frac12\)
. The group then assembles the scaled pieces and examines the accuracy of their scaled puzzle. Consider having students use a color in place of the cross hatching.
[IMG]
[IMG]
As students work, notice how they measure distances and whether they consider angles. Depending on how students determine scaled distances, they may not need to transfer angles. Look out for students who measure only the lengths of drawn segments rather than distances, e.g., between the corner of a square and where a segment begins. Suggest that they consider other measurements that might help them locate the beginning and end of a segment.
You will need the Scaling a Puzzle blackline master for this activity.
Teacher Notes for IM 6–8 Math Accelerated
If time allows, allow students to start this activity in class and then finish as part of the practice problem set.
Launch
Arrange students in groups of 3. Give pre-cut puzzle squares 1 and 5 to one student in the group, squares 2 and 6 to a second student, and squares 3 and 4 to the third. After students have answered the first question, give each student 2 blank squares cut from the second section of the blackline master, whose sides are half of the side length of the puzzle squares. Provide access to geometry toolkits.
Engagement: Develop Effort and Persistence.
Connect a new concept to one with which students have experienced success. Before students begin, ask them to predict which tools, from their geometry toolkits, they anticipate they will need, and to describe how they might use them. During the activity, make sure that students are using their rulers and protractors correctly.
Supports accessibility for: Visual-spatial processing; Conceptual processing; Fine-motor skills
Student Facing
Your teacher will give you 2 pieces of a 6-piece puzzle.
If you drew scaled copies of your puzzle pieces using a scale factor of
\(\frac12\)
, would they be larger or smaller than the original pieces? How do you know?
Create a scaled copy of each puzzle piece on a blank square, with a scale factor of
\(\frac12\)
.
When everyone in your group is finished, put all 6 of the original puzzle pieces together like this:
[IMG]
Next, put all 6 of your scaled copies together. Compare your scaled puzzle with the original puzzle. Which parts seem to be scaled correctly and which seem off? What might have caused those parts to be off?
Revise any of the scaled copies that may have been drawn incorrectly.
If you were to lose one of the pieces of the original puzzle, but still had the scaled copy, how could you recreate the lost piece?
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Anticipated Misconceptions
Students may incorporate the scale factor when scaling line segments but neglect to do so when scaling distances between two points not connected by a segment. Remind them that all distances are scaled by the same factor.
Students may not remember to verify that the angles in their copies must remain the same as the original. Ask them to notice the angles and recall what happens to angles when a figure is a scaled copy.
Activity Synthesis
Much of the conversations about creating accurate scaled copies will have taken place among partners, but consider coming together as a class to reflect on the different ways students worked. Ask questions such as:
How is this task more challenging than creating scaled copies of polygons on a grid?
Besides distances or lengths, what helped you create an accurate copy?
How did you know or decide which distances to measure?
Before your drawings were assembled, how did you check if they were correct?
Student responses to these questions may differ: for example, for piece 6, the two lines can be drawn by measuring distances on the border of the puzzle piece; the angles work out correctly automatically. For piece 2, however, to get the three lines that meet in a point in the middle of the piece just right, students can either measure angles, or extend those line segments until they meet the border of the piece (and then measure distances).


aligns: no