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: 
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_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
In this activity, students recall what they know about division from grade 3. The context allows students to connect lived experiences to the math of the activity. By inviting students to consider treats that they enjoy in their homes or neighborhoods, they share experiences and foster connections that build community.
The first question gives students an opportunity to co-craft mathematical questions based on a situation before answering a question based on a division equation. Students divide a two-digit number by a one-digit divisor, as they did in grade 3, in a way that makes sense to them. The activity synthesis highlights different representations students made and relates them to the situation. The term
dividend
is re-introduced in this lesson to describe a number being divided into equal groups.
This activity uses
MLR5 Co-craft Questions
. Advances: writing, reading, representing
Action and Expression: Develop Expression and Communication.
Give students access to concrete manipulatives (connecting cubes, counters, or square tiles) and grid paper. Invite students to use these to act out or draw
\(84 \div 7\)
.
Supports accessibility for: Conceptual Processing, Attention
Launch
Groups of 2
“What are some of your favorite treats or snacks from home?”
30 seconds: quiet think time
1 minute: partner discussion
MLR 5: Co-craft Questions
Display the opening paragraph and the first question.
“Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“How are these questions alike?” (The questions involve multiplying or dividing.) “How are they different?” (The questions can be answered using different operations.)
“Let’s look at the next question in the activity.”
Activity
3–4 minutes: quiet work time
Student Facing
Diego’s aunt is buying paletas, which are ice pops, for a class party. At the local market, paletas come in different flavors. She buys the same number of paletas of each flavor.
[IMG]
What mathematical questions can we ask about this situation?
Here is an equation:
\(84 \div 7 = {?}\)
In the situation about the class party, what questions could the equation represent?
Find the answer to one of the questions you wrote. Show your reasoning.
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
If students are unsure how to write a division question for
\(84 \div 7\)
, consider asking:
“If you were to act out the meaning of this expression, what would you do?”
“If you were to explain its meaning, what would you say?”
“In what type of situations would these types of actions take place?”
Activity Synthesis
Display two questions that students wrote for the equation
\(84 \div 7 = {?}\)
.
“What does the 84 represent in both problems?” (The amount being divided into equal groups.)
“In mathematics, the number being divided is known as the
dividend
.”
Invite students to share their strategies for the last question. Highlight strategies that show equal-size groups and reasoning that relates multiplication and division.


aligns: no