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: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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_pos_0

HS_0
standard_description: 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: Narrative
The purpose of this warm-up is to elicit the idea that expressions and equations can be used to represent different compositions and decompositions of 10, which will be useful when students match compositions and decompositions of 10 to equations in a later activity. While students may notice and wonder many things about these images and expressions, the fact that each image and expression represents a total of 10 is the important discussion point. Students have seen equations in previous lessons, but the synthesis is the first time that students are introduced to the term
equation
.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice?
What do you wonder?
[IMG]
\(7 + 3\)
[IMG]
\(5 + 5\)
[IMG]
\(8 + 2\)
Student Response
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Activity Synthesis
“What is the same about each expression?” (They are all 10.)
Write
\(10 = 7 + 3\)
.
“There are 10 counters, 7 red counters and 3 yellow counters. We can write that as 10 is 7 plus 3. When we write
\(10 = 7 + 3\)
, it is called an
equation
.”
Repeat the steps with the next 2 images.


aligns: no