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:
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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
problem_activity: Narrative
The purpose of this activity is for students to analyze a common error when using the standard algorithm to subtract decimals. This activity is recommended if students need additional practice with the standard algorithm when the two numbers do not have the same number of decimal places. The standard addition algorithm requires students to subtract digits with the same place value. In the given example the two numbers are “right aligned” as when subtracting whole numbers and this leads to the error of subtracting hundredths from tenths, tenths from ones, and so on as if these digits had the same place value.
When students identify and correct Elena's error they construct viable arguments and critique the reasoning of others (MP3).
This activity uses
MLR3 Clarify, Critique, and Correct
. Advances: Reading, Writing, Representing.
Launch
Groups of 2
Activity
1–2 minutes: quiet think time
6–8 minutes: partner work time
MLR3 Clarify, Critique, Correct
Display Elena’s solution and explanation.
Read the explanation aloud.
“What do you think Elena means? Is anything unclear?” (She says the answer will be less than 622.3, but she doesn’t say how much less. The answer will be a lot less than 615.21.)
“With your partner, work together to write a revised solution and explanation.”
(Optional) Display and review the following criteria:
Explanation of mistakes
Specific words and phrases
Decimal point
Place value
Labeled diagram
Correct solution
3–5 minutes: partner work time
Select 1–2 groups to share their revised explanation with the class.
“What is the same and different about the revised solutions and explanations?”
Student Facing
Find the value of
\(622.35 - 71.4\)
. Explain or show your reasoning.
Elena and Andre found the value of
\(622.35 - 71.4\)
. Who do you agree with? Explain or show your reasoning.
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If a student does not have a strategy to solve problem 1, ask them to explain how they would find the value of
\(622 - 51\)
.
Activity Synthesis
Display Andre’s solution and explanation.
“Why do you think Andre wrote 71.40 instead of 72.4?” (It helps him keep the place values and decimals in line so he doesn’t mix up the places when he is subtracting. 71.40 is equivalent to 71.4.)
Display Elena’s solution.
“How can you see without finding the difference that Elena’s answer is not correct?” (Taking 71 away from 622 is a lot less than 615.
\(620-70=550\)
so the answer should be around 550.)


aligns: no