few_shots: 
Example 1:
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.

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

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_pos_0

K

im_task_000157_pos_0

3

fl_problem_000674_pos_0

5
standard_description: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
problem_activity: Activity
In this activity, students first encounter exponential expressions with variables.
Launch
Recall with students that when we write
\(6x^2\)
, we mean to multiply 6 by the result of
\(x^2\)
. Remind them that the number part of such a product is called the
coefficient
of the expression, so in this example, 6 is the coefficient of
\(x^2\)
.
Give students 5 minutes of quiet work time to evaluate the expressions. Follow with whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts. After students have evaluated the first 2-3 expressions, check-in with either select groups of students or the whole class. Invite students to share the strategies they have used so far as well as any questions they have before continuing.
Supports accessibility for: Organization; Attention
Student Facing
Evaluate each expression for the given value of
\(x\)
.
\(3x^2\)
when
\(x\)
is 10
\(3x^2\)
when
\(x\)
is
\(\frac19\)
\(\frac{x^3}{4}\)
when
\(x\)
is 4
\(\frac{x^3}{4}\)
when
\(x\)
is
\(\frac12\)
\(9+x^7\)
when
\(x\)
is 1
\(9+x^7\)
when
\(x\)
is
\(\frac12\)
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 use the wrong order when evaluating expressions, such as in multiplying by 3 first in
\(3x^2\)
and then squaring. Have them recall the last lesson where they practiced applying the agreed on order of operations in numeric expressions.
Students may interpret an expression like
\(3x\)
as meaning 3 next to the digit
\(x\)
instead of as multiplication. For example, students may think that
\(3x\)
means 35 instead of 15 when
\(x=5\)
. Discuss how the shorthand notation of coefficients next to variables with no symbols between them tells us to multiply, and that it will simplify future work with expressions and equations.
Activity Synthesis
The purpose of the discussion is to ensure that students understand how to evaluate expressions with variables for a given value of the variable. It is also an opportunity for students to practice interpreting and using vocabulary like
coefficient, variable,
power,
and
exponent
.
Some guiding questions:
"In each expression, what is the coefficient?" (3, 3,
\(\frac14\)
,
\(\frac14\)
, 1, 1.)
"Choose one of the expressions. Describe the steps that you carried out to evaluate the expression." (Sample response: I rewrote
\(9+x^7\)
as
\(9+\left(\frac12\right)^7\)
. I needed to first evaluate the exponent. I knew that
\(\left(\frac12\right)^7\)
means
\(\frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12\)
, which is
\(\frac{1}{128}\)
. So then I wrote
\(9 + \frac{1}{128}\)
, which can also be written
\(9\frac{1}{128}\)
.
"How is evaluating the expressions when
\(x\)
is a fraction similar to when
\(x\)
is a whole number?  How is it different?" (It's similar because you're still just multiplying
\(x\)
by itself a certain number of times. It's different because multiplying a fraction by a fraction is a bit more complicated than multiplying a whole number by itself.)
Speaking, Writing: MLR8 Discussion supports.
Use this to amplify mathematical uses of language to communicate about how to evaluate exponential expressions. Revoice the term “coefficient” during student discussion and press for detail when identifying the coefficients and the order in which they are multiplied in each expression.
Design Principle(s): Support sense-making


aligns: no