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.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

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} $

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.

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

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?


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.

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, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_neg_0

K

im_task_000157_neg_0

3

fl_problem_000674_neg_0

5
standard_description: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
problem_activity: Activity
Students may be familiar with this proof from middle school. Revisiting this proof helps students connect a familiar diagram and proof to the similarity proof. It also gives students an opportunity to compare and contrast different types of proof and think about why mathematicians might bother to re-prove something that has already been proved.
Launch
Use the Notice and Wonder routine to help students make sense of the context and images they will be using. Ask students what they notice and wonder about the images. If not mentioned by students, ask where
\(c\)
shows up in these images.
Writing, Listening, Conversing: MLR1 Stronger and Clearer Each Time.
Use this routine to help students improve their written responses for how Pythagoras used the diagrams to prove
\(a^2+b^2=c^2\)
. Give students time to meet with 2–3 partners to share and receive feedback on their responses. Display feedback prompts that will help students strengthen their ideas and clarify their language. For example, “How do you know that the two large squares are the same size?”, and “How do you know that the area of the blue square is
\(c^2\)
?” Invite students to go back and revise or refine their written responses based on the feedback from peers. This will help students justify the proof of the Pythagorean Theorem.
Design Principle(s): Optimize output (for justification); Cultivate conversation
Representation: Develop Language and Symbols.
Use virtual or concrete manipulatives to connect symbols to concrete objects or values. Provide access to the different pieces of the figures so students can rearrange and compare them.
Supports accessibility for: Visual-spatial processing; Conceptual processing
Student Facing
[IMG]
When Pythagoras proved his theorem he used the 2 images shown here. Can you figure out how he used these diagrams to prove
\(a^2+b^2=c^2\)
in a right triangle with hypotenuse length
\(c\)
?
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?
James Garfield, the 20th president, proved the Pythagorean Theorem in a different way.
Cut out 2 congruent right triangles
Label the long sides
\(b\)
, the short sides
\(a\)
and the hypotenuses
\(c\)
.
Align the triangles on a piece of paper, with one long side and one short side in a line. Draw the line connecting the other acute angles.
How does this diagram prove the Pythagorean Theorem?
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Encourage students to look for
\(a^2\)
. Students have scissors and tracing paper in their geometry toolkits, they may want to trace, cut out, and reassemble the pieces.
Activity Synthesis
Invite students to talk about the differences between this proof and the one in the previous activity, including which one made more sense to them, which one they preferred writing, or which one felt most convincing. Ask students why they think mathematicians might continue to try to come up with different ways to prove a theorem as old as the Pythagorean Theorem.


aligns: yes