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 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_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this activity is for students to apply what they learned in earlier lessons to represent a division situation. During the synthesis, students connect what they know about division to multiplication when they see that the situation of 2 people equally sharing the distance in a 3 mile race can also be described as each person running one-half of the three mile race. Students connect the language they used to describe the situation to multiplication and division expressions. This relationship between multiplication and division is the focus of the next several lessons.
This activity uses
MLR2 Collect and Display.
Advances: Conversing, Reading, Writing.
Launch
Display the image from the student workbook.
“Tell a story about this image to your partner.”
“This image shows two children who are running in a relay race. They are on the same team. They each have to run the same distance. The boy holding the baton is finishing his turn. When he hands the baton to his teammate, his teammate will take her turn.”
Activity
Groups of 2
2 minutes: independent think time
5–8 minutes: partner work time
MLR2 Collect and Display
Circulate, listen for and collect the language students use to describe how to represent the situation and how far each person ran.
Listen for:
3 miles divided into 2 parts
half of 3 miles
one and one half miles
three halves
Record students’ words and phrases on a visual display and update it throughout the lesson.
Student Facing
[IMG]
Lin and Han ran a 3 mile relay race as a team. They each ran the same distance. Draw a diagram to represent the situation.
Take turns describing to your partner how your diagrams represent the situation.
How far did each person run?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“These are the words and phrases that you used to describe the situation. 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.
Display:
\(3 \div 2\)
,
\(1\frac{1}{2}\)
,
\(\frac{3}{2}\)
, and
\(3\times \frac{1}{2}\)
“How does each of these expressions represent the situation?” (3 miles was divided into 2 equal parts, each person ran
\(1\frac{1}{2}\)
miles or
\(\frac{3}{2}\)
miles which can be thought of as
\(3\times \frac{1}{2}\)
.
Consider giving students time to record their answers in their journal.
Display: “one half of 3 miles”
“This is another way to describe how far each person ran.”
Display:
\(\frac{1}{2}\times3\)
“We can also use this multiplication expression to represent one-half of 3.”
“In the next activity, you will describe how different diagrams represent each of these expressions.”


aligns: no