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: 
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_neg_0

K

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
problem_activity: Activity
Having just seen an example of the meaning of
\(a\)
and
\(b\)
in an exponential expression
\(a \boldcdot b^x\)
, students now focus on interpreting these numbers using graphs. They graph the equations from the previous task, noticing that
\(a\)
is the vertical intercept of the graph while the number
\(b\)
determines how quickly the graph grows (since in these cases
\(b>1\)
). A larger value of
\(b\)
corresponds to a more rapid rate of growth for the bacteria population. The axes for the graphs have been labeled here, but in future activities, students will have to think strategically about how to label the axes to most effectively plot the points.
Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Display the equations from the previous activity for all to see (if they are not already visible).
Conversing: MLR8 Discussion Supports.
Use this routine to help students describe the meaning of variables in exponential expressions. Arrange students in groups of 2. Invite Partner A to share their observations for the first graph and Partner B to share their observations for the second graph. Provide sentence frames such as “I can connect the equation to the graph by….” and “I notice that….” Invite the listener to press for additional details referring to features of the graphs, such as the vertical intercept, specific points, and the steepness of the curve. This will help students justify how features of the graph can be used to identify matching equations.
Design Principle(s): Support sense-making; Cultivate conversation
Student Facing
Refer back to your work in the table of the previous task. Use that information and the given coordinate planes to graph the following:
a. Graph
\((t,n)\)
when
\(t\)
is 0, 1, 2, 3, and 4.
[IMG]
b. Graph
\((t,p)\)
when
\(t\)
is 0, 1, 2, 3, and 4. (If you get stuck, you can create a table.)
[IMG]
On the graph of
\(n\)
, where can you see each number that appears in the equation?
On the graph of
\(p\)
, where can you see each number that appears in the equation?
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
Students may have trouble graphing the points, particularly finding the appropriate vertical (
\(n\)
or
\(p\)
) values. Ask them to find the coordinates of the grid points on the vertical axis and use that to estimate the vertical position of their points.
When calculating values by hand, many students may mistakenly write an expression like
\(100 \boldcdot 3^2\)
as
\(300^2\)
. Remind them that the expression
\(100 \boldcdot 3^2\)
means
\(100 \boldcdot 3 \boldcdot 3\)
.
Activity Synthesis
Make sure students recognize two key takeaways from this activity:
The vertical intercept of the graph is the initial bacteria population size. It is the size of the population when first measured, or when
\(t\)
, the number of hours since measurement, is 0.
The growth factor of the populations is represented by how quickly the graph increases.


aligns: yes