few_shots: 
Example 1:
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.

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.


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

Example 2:
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.

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} $

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

Example 3:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

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?


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_neg_0

K

im_task_000157_pos_0

3

fl_problem_000674_pos_0

5
standard_description: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
problem_activity: Activity
The mathematical purpose for this activity is to allow students to practice solving for a variable in an equation with two variables. In the associated Algebra lesson, expressing one variable in terms of another is necessary before substituting an expression for a variable in another equation.
Launch
Demonstrate how to solve for a variable by showing students the equation
\(a + 2b = 5\)
. Solving for
\(a\)
results in
\(a = 5 - 2b\)
or
\(a = \text{-}2b + 5\)
. Solving for
\(b\)
results in
\(b = \frac{5-a}{2}\)
or
\(b = \frac{5}{2} - \frac{a}{2}\)
or another equivalent expression.
Student Facing
Solve for the indicated variable.
Solve for
\(k\)
.
\(2t+k=6\)
Solve for
\(n\)
.
\(10n=2p\)
Solve for
\(c\)
.
\(12-6d=3c\)
Solve for
\(g\)
.
\(h=8g+4\)
Solve for
\(x\)
.
\(4x+3y=12\)
Solve for
\(y\)
.
\(4x+3y=12\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The purpose of the discussion is to share strategies for solving for one variable in an equation including more than one variable. Select students to share their answers and strategies. As students share, consider asking another student why each step makes sense to do.
Some questions for discussion:
"How do you know when you are done solving for a variable?" (When the variable I want to solve for is the only thing on one side of the equation.)
"How is solving for
\(x\)
in an equation like
\(4x+3y=12\)
similar or different from solving for
\(x\)
in an equation like
\(4x + 6 = 12\)
?" (The steps are very similar, but when there is only one variable, we can know the value of
\(x\)
that makes the equation true.)
"If you know the value for
\(y\)
is 2 and need to know the value for
\(x\)
, would you rather begin with the equation
\(4x + 3y = 12\)
or the equivalent equation
\(x = 3 - \frac{3}{4}y\)
? Explain your reasoning." (I would rather use the second equation since I only need to substitute in the value for
\(y\)
and evaluate the expression rather than solve an equation.)


aligns: yes