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: 
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.

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

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: 
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.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_001477_pos_0

K

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
problem_activity: Optional activity
The goal of this task is to introduce the notion of a tessellation and then carefully examine how to create a tessellation with each pattern block shape (square, rhombus, equilateral triangle, isosceles trapezoid). For hexagons, there is only one way to fit them together because there will be gaps unless three hexagons meet at each vertex. The other shapes offer much more flexibility, and students have an opportunity to use their artistic creativity.
Students look for and make use of structure (MP7), both when they try to put copies of the shape together to build a tessellation and when they examine whether or not it is possible to construct a different tessellation.
Digital
Launch
Introduce the definition of a
tessellation
of the plane by polygons: a tessellation covers the plane with copies of the shape with no gaps and no overlaps.
Show the students the image from the previous notice and wonder activity, and ask them if these are tessellations. (Yes.)
Demonstrate how to use tracing paper to create a tessellation.
Arrange students in groups of 2. Each pair uses the same shape for their tessellations.
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Include the following term and maintain the display for reference throughout the lesson: tessellation. Consider providing step-by-step directions for students to use tracing paper to create a tessellation. Invite students to suggest language or diagrams to include that will support their understanding.
Supports accessibility for: Memory; Language
Speaking: MLR8 Discussion Supports.
Amplify students' uses of mathematical language to communicate about tessellations; edge to edge, vertex, symmetrical, plane, rigid motion, etc. Encourage students to use these words, revoicing students’ ideas as necessary. Ask students to chorally repeat the phrases that include these words in context.
Design Principle(s): Support sense-making; Optimize output (for explanation)
Student Facing
With your partner, choose one of the six shapes in the toolbar that you will both use.
Select the shape tool by clicking on it. Create copies of your shape by clicking in the work space.
When you have enough to work with, click on the Move tool (the arrow) to drag or turn them.
If you have trouble aligning the shapes, right click to turn on the grid.
When you are finished making your tessellation, you can hide the points.
Compare your tessellation to your partner’s. How are they similar? How are they different?
If possible, make a third tessellation of the plane with your shape (different from the ones you and your partner already created). If not possible, explain why it is not possible.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Introduce the definition of a
tessellation
of the plane by polygons: a tessellation covers the plane with copies of the shape with no gaps and no overlaps.
Show the students the image from the previous notice and wonder activity, and ask them if these are tessellations. (Yes.)
Demonstrate how to use tracing paper to create a tessellation.
Arrange students in groups of 2. Each pair uses the same shape for their tessellations.
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Include the following term and maintain the display for reference throughout the lesson: tessellation. Consider providing step-by-step directions for students to use tracing paper to create a tessellation. Invite students to suggest language or diagrams to include that will support their understanding.
Supports accessibility for: Memory; Language
Speaking: MLR8 Discussion Supports.
Amplify students' uses of mathematical language to communicate about tessellations; edge to edge, vertex, symmetrical, plane, rigid motion, etc. Encourage students to use these words, revoicing students’ ideas as necessary. Ask students to chorally repeat the phrases that include these words in context.
Design Principle(s): Support sense-making; Optimize output (for explanation)
Student Facing
[IMG]
Pick one of the shapes. Create a
tessellation
by tracing copies of your shape. Make sure to use the same shape as your partner.
Compare your tessellation to your partner’s. How are they similar? How are they different?
If possible, make a third tessellation of the plane with your shape (different from the ones you and your partner already created). If not possible, explain why it is not possible.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Tessellations do not need to be edge to edge. That is, pieces do not need to fit together with edges of the same lengths matching exactly.
Tessellations do not need to have symmetric, repeating patterns, though sometimes the shape forces it (as with the regular hexagons).
Activity Synthesis
Important questions to address include:
“Were you able to make different tessellations with your shape?” (It depends on the shape.)
“If not, why not?” (Three hexagons have to come together at each vertex: once the first hexagon of the pattern is placed, everything else has no flexibility.)
“If so how?” (Triangles can be built into hexagons, or they can make rows that can be translated and stacked on top of one another. Parallelograms can also be made into hexagons or rows. Trapezoids can be made into hexagons or rows. Rhombuses can be made into rows and translated. Squares can also be made into rows and translated.)
“What does it look like to
not
define a tessellation?” (Two octagons can be put together sharing a vertex, but there is a gap that is not large enough for a third octagon.)
Make sure, as students share their ideas for tessellations, to use the language of rigid motions to describe the tessellations. For example, if a student has built a tessellation with parallelograms, choose two parallelograms and ask:
“How can I use rigid motions to move one of these parallelograms into the position of the other?”
“Are there other ways I could do this?”


aligns: no