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 multiply multi-digit whole numbers using the standard algorithm.

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

shot_info: im_task_001477_pos_0

K

im_task_000157_pos_0

3

fl_problem_000674_pos_0

5
standard_description: Use the structure of an expression to identify ways to rewrite it. For example, see x^(4) – y^(4 )as (x^(2))^(2 )– (y^(2))^(2), thus recognizing it as a difference of squares that can be factored as (x^(2 )– y^(2))(x^(2 )+ y^(2)).
problem_activity: Activity
In this activity, students solve a system of equations by graphing then include a third line through the solution point that is either vertical or horizontal. In the associated Algebra lesson, students will graph equations in a system and additional equations that arise from the elimination method to show that they all intersect at the solution.
To focus on the work of the activity, it is recommended that students use the digital version of the activity or have access to Desmos or another graphing tool to more quickly and accurately find the solutions to the system of equations through graphing. If students need practice graphing lines representing equations by hand or if digital access is not available, the print version provides a graph given one of the lines and asks students to graph the second line by hand.
Launch
Display the instructions for all to see. Ask students,
"What do you know about equations that are represented by vertical lines?" (They are of the form
\(x = a\)
for a number
\(a\)
.)
"What do you know about equations that are represented by horizontal lines?" (They are of the form
\(y = a\)
for a number
\(a\)
.)
Student Facing
For each system of equations:
Solve the system of equations by graphing. Write the solution as an ordered pair.
Write an equation that would represented by a vertical or horizontal line that also passes through the solution of the system of equations.
Graph your new equation along with the system.
\(\begin {cases} \begin {align}y = 3x+5\\ y=\text{-}x+1\end{align} \end {cases}\)
The line representing
\(y = 3x+5\)
is shown
[IMG]
\(\begin {cases} \begin {align}y = \frac{1}{3}x-2\\ y=x-6\end{align} \end {cases}\)
The line representing
\(y = \frac{1}{3}x-2\)
is shown
[IMG]
\(\begin {cases} \begin {align} 2x+3y=10\\ x+y=3\end{align} \end {cases}\)
The line representing
\(2x+3y=10\)
is shown
[IMG]
Student Response
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Activity Synthesis
The purpose of the discussion is for students to recognize that, for a system of equations represented by graphs that intersect at
\((a,b)\)
, the lines
\(x = a\)
and
\(y = b\)
also go through the solution. Select students to share their solutions including students who found vertical as well as horizontal lines through the intersection point.
Some questions for discussion:
"How could you use your answers to these questions to write another system of equations that have the same solution as the original system of equations?" (The system
\(\begin {cases} \begin {align} x = \text{-}1\\ y=2\end{align} \end {cases}\)
has the same solution as the original equation
\(\begin {cases} \begin {align}y = 3x+5\\ y=\text{-}x+1\end{align} \end {cases}\)
since all 4 lines go through the point
\((\text{-}1,2)\)
.)
"Two lines intersect at the point
\((3,5)\)
. How could you know whether the equation
\(3x - 2y = \text{-}1\)
is represented by a line that goes through that same point?" (Substitute the value 3 for
\(x\)
and 5 for
\(y\)
. If the equation is still true, then the associated line will go through the same point. If the equation is false, the associated line will not go through the same point.)


aligns: no