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:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
problem_activity: Optional activity
The purpose of this activity is for students to find a fractional percent increase.
Look for students who calculate the percentage first and then add them together, and students who multiply by 1.08 and 1.008, respectively.
Launch
Students in groups of 2. 4 minutes of quiet work time followed by partner and then whole-class discussion.
Representation: Internalize Comprehension
. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?
The population of city B was approximately 7,150,000, and it increased by 0.8% in one year. What was the new population?
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 who want to multiply by
\(1 + \frac{p}{100}\)
may have trouble determining where to put the decimal. Have them think about the problem in steps. How can you find 8%? (Multiply by 0.08.) How can you find 0.8%? (Multiply by 0.008.)
Activity Synthesis
Have selected students show solutions, starting with a solution where the percentage is found first and then added to the initial amount, then the approach where one multiplies by 1.08 or 1.008, respectively. Make sure everyone understands both methods. Help students see the connections between these strategies.
Representing, Speaking: MLR7 Compare and Connect.
Use this routine after students present their solutions for calculating the new population of each city. Ask students, "what is the same and what is different about these approaches?" Call students' attention to the different ways students represented the percent increase in their strategies. These exchanges strengthen students' mathematical language use and reasoning based on percent increases with and without fractional amounts.
Design Principle(s): Maximize meta-awareness


aligns: no