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: 
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 problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_neg_0

5
standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Activity
In this activity, students find intercepts and slopes for pairs of equations. They should notice that the equations in each pair are multiples of one another and therefore are equivalent equations. Students look for and make use of structure (MP7) when they notice the relationships between the pairs of equations.
Launch
Ask students what they remember about
\(x\)
- and
\(y\)
-intercepts. One useful thing to remember is that the
\(x\)
-intercept of a graph occurs where the
\(y\)
-coordinate is zero. (Demonstrate using a graph, if needed.) So, to find the
\(x\)
-intercept of a graph representing an equation, you can replace
\(y\)
with 0 and solve the equation for
\(x\)
. (And vice versa to find the
\(y\)
-intercept.)
Ask students how they can use two points like
\((1,0)\)
and
\((0,8)\)
to find the slope of a line. (Using a formula like
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
, or a less-formal version like “subtract the y’s, subtract the x’s, then divide.
”
For this example the slope is -8 since
\(\frac{8 - 0}{0-1} = \text{-}8\)
.)
Student Facing
Here are some equations in pairs. For each equation:
Find the
\(x\)
-intercept and
\(y\)
-intercept of a graph of the equation.
Find the slope of a graph of the equation.
\(x + y = 6\)
and
\(2x + 2y = 12\)
\(3y - 15x = \text{-}33\)
and
\(y - 5x = \text{-}11\)
\(5x + 20y = 100\)
and
\(4x + 16y = 80\)
\(3x - 2y = 10\)
and
\(4y - 6x = \text{-}20\)
What do you notice about the pairs of equations?
Choose one pair of equations and rewrite them into slope-intercept form (
\(y = mx + b\)
). What do you notice about the equations in this form?
Student Response
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Activity Synthesis
The purpose of the discussion is to show that equations that are multiples of one another will have graphs with the same intercepts and slope. Select students to share their solutions and methods for finding the intercepts and slope as well as things they notice. While students may notice many things, ensure it is mentioned that in each pair of equations, one is a multiple of the other.
Some questions for discussion:
"How would the graphs of each pair of equations look?" (Each graph would look like a single line since the two equations are equivalent. Time permitting, demonstrate this using graphing technology.)
"Select a pair of equations. Find another equation whose graph would have the same slope and intercepts as the pair already given." (Another multiple of either equation will work.)


aligns: yes