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 following problem or activity 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: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
problem_activity: Activity
In the previous activity, students interpreted given tape diagrams and explained how they represented a story. Here, they have a chance to draw tape diagrams to represent a story. The first story is a bit more scaffolded because it specifies what
\(x\)
represents. In the other two stories, students need to decide which quantity to represent with a variable and choose a letter to use. As with all activities in this lesson, students are
not
expected to write and solve an equation. This preliminary work supports the understanding needed to be able to represent such situations with equations.
Digital
Launch
Keep students in the same groups. You might have
each
student draw
all three
diagrams and compare them with their groups, working together to resolve any discrepancies. Or if time is short, you might assign
each
student in the group
a different story—
ask each student to explain their diagram to their group to see if their group members agree with their interpretation.
For classrooms using the digital version of the materials, take a minute to demonstrate how the controls work in the applet. Some students may prefer to draw the diagrams in their notebooks or on scratch paper.
Action and Expression: Internalize Executive Functions.
Provide students with a blank template of a tape diagram to represent each story.
Supports accessibility for: Language; Organization
Student Facing
Here are three more stories. Draw a tape diagram to represent each story. Then describe how you would find any unknown amounts in the stories.
Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts
\(x\)
stickers in each bag. After filling 4 bags, they have used a total of 44 items.
Noah’s family also wants to blow up a total of 60 balloons for the party. Yesterday they blew up 24 balloons. Today they want to split the remaining balloons equally between four family members.
Noah’s family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Keep students in the same groups. You might have
each
student draw
all three
diagrams and compare them with their groups, working together to resolve any discrepancies. Or if time is short, you might assign
each
student in the group
a different story—
ask each student to explain their diagram to their group to see if their group members agree with their interpretation.
For classrooms using the digital version of the materials, take a minute to demonstrate how the controls work in the applet. Some students may prefer to draw the diagrams in their notebooks or on scratch paper.
Action and Expression: Internalize Executive Functions.
Provide students with a blank template of a tape diagram to represent each story.
Supports accessibility for: Language; Organization
Student Facing
Here are three more stories. Draw a tape diagram to represent each story. Then describe how you would find any unknown amounts in the stories.
Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts
\(x\)
stickers in each bag. After filling 4 bags, they have used a total of 44 items.
Noah’s family also wants to blow up a total of 60 balloons for the party. Yesterday they blew up 24 balloons. Today they want to split the remaining balloons equally between four family members.
Noah’s family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Design a tiling that uses a repeating pattern consisting of 2 kinds of shapes (e.g., 1 hexagon with 3 triangles forming a triangle). How many times did you repeat the pattern in your picture? How many individual shapes did you use?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Much of the discussion will take place in groups. Here are some ideas for synthesizing students’ learning about creating tape diagrams:
Ask students if they had any disagreements in their groups and how they resolved them.
Ask students how they decided which unknown quantity to find in the story. The first story specifies
\(x\)
stickers, but the other stories do not define a variable.
Display one diagram for each story and ask students to explain how they are alike and how they are different.


aligns: no