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 to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

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_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
- 100 can be thought of as a bundle of ten tens — called a “hundred.”
- The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
problem_activity: Narrative
In this activity, students identify the nearest multiples of 10 and 100 for given three-digit numbers. They may do so by using the number lines from earlier, but they may also start to notice a pattern in the relationship between the numbers and the nearest multiples and decide not to use number lines. The work here prepares students to reason numerically in the next lesson.
When students notice and describe patterns in the relationship between the numbers and the nearest multiples of 10 or 100, they look for and express regularity in repeated reasoning (MP8).
MLR2 Collect and Display:
Circulate, listen for, and collect the language students use as they make sense of “close to” and “about.” On a visible display, record words and phrases such as: “almost 100, but not exactly,” “only 1 away from 100,” “less than 5 away.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Launch
Groups of 2
“Let's find more multiples of 10 and 100 that are close to some numbers.”
“Notice that no number lines are given. See if you can still find the nearest multiples of 10 and 100 without them. If you need to, you can still use a number line.”
Activity
“Work with your partner to complete these problems.”
5–7 minutes: partner work time
Monitor for students who use the following strategies to highlight:
Reason about the midpoint between a multiple of 10 or a multiple of 100 (5 or 50) to determine which multiple is closer, such as, “568 is closer to 570 because 565 would be the middle point between 560 and 570.”
Use place value patterns to determine which multiple is closer, such as, “Since the 1 in 712 is less than 5, it tells me that the number is closest to 700.”
Pause for a brief discussion before students complete the last problem.
Select previously identified students share the strategies they used to find the nearest multiple of 100 and the nearest multiple of 10.
“Now take a few minutes to complete the last problem.”
2–3 minutes: independent work time
Student Facing
Is 349 closer to 300 or 400?
Is 349 closer to 340 or 350?
Is 712 closer to 700 or 800?
Is 712 closer to 710 or 720?
Is 568 closer to 500 or 600?
Is 568 closer to 560 or 570?
Without locating a given number on a number line, how did you decide:
the nearest multiple of 100?
the nearest multiple of 10?
Name the nearest multiple of 100 and the nearest multiple of 10 for:
324
89
Student Response
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Advancing Student Thinking
If students don’t identify the closest multiple of 10 or 100, consider asking:
“What have you tried to find the closest multiple of 10 (or 100)?”
“How could you use a number line to find the closest multiple of 10 (or 100)?”
Activity Synthesis
Invite students to share their responses and reasoning for the last problem.


aligns: no