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 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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to interpret and compare representations that show decomposing a ten to subtract by place. One student shows decomposing a ten by crossing off a ten and drawing 10 ones. The other representation shows a student who begins their drawing with a ten decomposed into 10 ones. Students compare and make connections between the representations and a set of equations that also shows how to find the value of the difference (MP3).
This activity uses
MLR2 Collect and Display
. Advances: conversing, reading, writing
Representation: Internalize Comprehension.
Invite students to identify which details were most useful from each strategy to solve the problem. Display the sentence frame, “The next time I have a subtraction task, I will look for . . . .“ Encourage decomposition, drawing pictures or using manipulatives as the main strategies.
Supports accessibility for: Attention, Memory
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“Diego and Elena drew base-ten diagrams to find the value of
\(82-9\)
.”
“Think about what is the same or different on your own. Then, discuss your ideas with your partner.”
1 minute: quiet think time
2
–
3 minutes: partner discussion
MLR2 Collect and Display
Circulate, listen for, and collect the language students use to describe the diagrams and how the ten is decomposed. Listen for: break apart a ten, decompose, tens, need more ones.
Record students’ words and phrases on a visual display and update it throughout the lesson.
Share responses. Consider asking:
“Did Diego and Elena find the same value for
\(82-9\)
? How do you know?”
“What is the difference between their diagrams?”
“Tyler found the value by using equations. Diego says Tyler’s equations match his diagram. Elena says the equations match her diagram. Who do you agree with?”
2 minutes: independent work time
4 minutes: partner discussion
Monitor for students who agree with Diego, Elena, or both and can explain their reasoning with connections to the diagrams.
Student Facing
Diego and Elena drew base-ten diagrams to find the value of
\(82-9\)
.
Diego
[IMG]
Elena
[IMG]
Compare Deigo’s work to Elena’s.
What is the same?
What is different?
Tyler used equations to show his thinking.
\(82 - 9\)
\(82 = 70 + 12\)
\(12 - 9 = 3\)
\(70 + 3 = 73\)
Diego says Tyler’s work matches his diagram.
Elena says Tyler’s work matches her diagram.
Who do you agree with? Explain.
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
Some students may only recognize 82 as 8 tens and 2 ones. Consider asking:
“What was the value of Elena’s blocks before she started subtracting? Explain.”
“How could you make 82 with base-ten blocks if you only had 7 tens?” Allow students to share how they could represent 82 with 7 tens and 12 ones.
Activity Synthesis
Invite previously identified students to share.
“Diego, Elena, and Tyler saw they needed more ones before they could subtract ones from ones. They showed decomposing a ten in different ways.”
Display the list of words and phrases recorded during the activity.
“Here are some of the words we used to describe subtracting by place.”
“Are there any other words or phrases that are important to include on our display?”
As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
Remind students to borrow language from the display as needed.


aligns: no