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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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
$$-\frac{1}{4}$$


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Thought: 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).
Answer: B

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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Estimate lengths using units of inches, feet, centimeters, and meters.
problem_activity: Narrative
The purpose of this activity is to introduce the foot as a length unit in the U.S. customary system. Students learn that a foot is longer than an inch and is the same length as 12 inches. They use the length of 12-in rulers as a tool to measure lengths in feet by iterating the length of a ruler, or, more precisely, the length of 12 inches shown on the ruler. The experience iterating lengths of a ruler to measure a length in feet helps students build a mental benchmark for the approximate length of a foot that they can use to estimate lengths.
Students measure lengths of tape that represent realistic lengths of different types of fish. They measure each length to the nearest inch and to the nearest foot. In the synthesis, students discuss the difference in their measurements and relate the differences to the size of the length units (MP7).
MLR2 Collect and Displa
y. Circulate, listen for, and collect the language students use as they measure the length of each animal. Display measurement words and comparative language such as: “inches,” “feet,” “ruler,” “more than,” “less than,” “longer,” “shorter,” “smaller,” and so on. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Required Materials
Materials to Gather
Inch tiles
Rulers (inches)
Tape (painter's or masking)
Required Preparation
Tape strips of these lengths on the floor. Label each strip with the letter and fish name. It may be helpful to make multiple sets of these lines to keep the groups small.
Strip A, largemouth bass: 2 feet
Strip B, spiny dogfish shark: 4 feet
Strip C, catfish: 3 feet
Strip D, koi: 2 feet and 6 inches
Launch
Groups of 3–4
Give each student an inch ruler and access to inch tiles.
“You have measured the length of objects and the sides of shapes using inches. If you are measuring longer objects, like the fish in the warm-up, you might want to use a different unit.”
“A
foot
is a longer length unit in the U.S. Customary Measurement System. A foot is the same length as 12 inches.”
“When we measure a length that starts at 0 on the ruler and ends at the 12, we can say the length is 12 inches or we can say the length is 1 foot.”
“What are some things you see around the classroom that are about 1 foot long?"
30 seconds: quiet think time
Share responses.
Activity
Display the images of the fish.
“In previous lessons, we measured the lengths of different kinds of reptiles. In this lesson, you will be measuring the lengths of fish. What do you know about fish?”
Share responses.
“Let’s imagine we work at the aquarium and need to measure the lengths of these fish. The tape on the floor represents their lengths.”
“Look at the tape strips on the floor. Use your rulers to measure each length first in feet. Then measure the length in inches using the rulers or your inch tiles.”
10 minutes: group work time
As needed, pause after students have measured their first fish in feet and invite students to share how they used their rulers to measure in feet.
Student Facing
Work with your group to measure the tape strips around the classroom in feet. Then measure the length in inches.
Tape A
largemouth bass
[IMG]
Length in feet: __________
Length in inches: __________
Tape B
spiny dogfish shark
[IMG]
Length in feet: __________
Length in inches: __________
Tape C
catfish
[IMG]
Length in feet: __________
Length in inches: __________
Tape D
koi
[IMG]
Length in feet: __________
Length in inches: __________
What did you notice about the number of feet compared to the number of inches when you measured the tape strips?
Student Response
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Advancing Student Thinking
If students measure lengths in feet by lining up multiple rulers or iterating the same ruler without considering gaps that may be caused by the lengths of the ruler before the 0 in or after the 12 in mark, point out these gaps on the ruler and consider asking:
“Can you show me how you measured the length of the ______ in feet?”
“Did you measure the length without any gaps? How do you know?”
“How would you revise the way you measure to make sure you have no gaps or overlaps?”
Activity Synthesis
“What did you notice about your measurements when you switched from measuring in feet to measuring in inches?” (The numbers are smaller for the number of feet. I had to count more inches than feet.)
“Why are our measurements in feet so much smaller than our measurements in inches?” (Feet are longer, so you don't need as many to measure the length of the tape. It takes more inches to cover the same length.)


correct_option_index: 0

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