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:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

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_neg_0

K

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
problem_activity: Activity
In this activity, students create two-way tables displaying relative frequency. The relative frequency table converts the actual frequency data to percentages which can be useful when comparing groups that include different totals. Finally, students use the relative frequencies to look for a pattern in the data. In the following lesson, students will work with associations in categorical data more explicitly. In this activity, students should use an informal understanding of association to think about whether one is present in the data based on the relative frequency table.
Launch
Keep students in groups of 2–3. After an introduction to relative frequency tables, allow students 3 minutes quiet work time followed by partner discussion and whole-class discussion.
Display the table for all to see.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}}, {"_attributes": {"scope": "col"}, "_value": "watch the news daily"}, {"_attributes": {"scope": "col"}, "_value": "does not watch the news daily"}, {"_attributes": {"scope": "col"}, "_value": "total"}]}]}], "tbody": [{"tr": [{"th": [{"_value": "younger than 18"}], "td": [{"_value": "30"}, {"_value": "80"}, {"_value": "110"}]}, {"th": [{"_value": "18 or older"}], "td": [{"_value": "10"}, {"_value": "5"}, {"_value": "15"}]}, {"th": [{"_value": "total"}], "td": [{"_value": "40"}, {"_value": "85"}, {"_value": "125"}]}]}]}]}
Ask students, "Based on this data, who is more likely to watch the news daily: someone who is younger than 18 or someone who is 18 or older?"
Tell students that, based on the numbers in the table, there are more younger people who watch the news (30) than older (10). On the other hand, the survey reached out to 110 young people and only 15 older people. Without looking at the whole table, that information may have been missed.
In cases like this, finding a relative frequency including percentages can be more helpful than looking at the actual frequency, which is what they are going to do now.
Use MLR 2 (Collect and Display) to co-create a graphic organizer with students comparing and contrasting the definitions and characteristics of “actual frequency” and “relative frequency” to be referenced and revised throughout this and later activities.
Conversing, Representing, Writing: MLR2 Collect and Display.
As students work in groups, capture the vocabulary and phrases students use when comparing and contrasting the definitions and characteristics of “actual frequency” and “relative frequency.” Listen for students who identify pros and cons for each representation and when one is preferable compared to the other. Record their language on a visual display that can be referenced in future discussions. This routine provides feedback to students that supports sense-making and increases meta-awareness of mathematical language.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
Here is a two-way table that shows data about cell phone usage among children aged 10 to 18.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}}, {"_attributes": {"scope": "col"}, "_value": "has cell phone"}, {"_attributes": {"scope": "col"}, "_value": "does not have cell phone"}, {"_attributes": {"scope": "col"}, "_value": "total"}]}]}], "tbody": [{"tr": [{"th": [{"_value": "10 to 12 years old"}], "td": [{"_value": "25"}, {"_value": "35"}, {"_value": "60"}]}, {"th": [{"_value": "13 to 15 years old"}], "td": [{"_value": "40"}, {"_value": "10"}, {"_value": "50"}]}, {"th": [{"_value": "16 to 18 years old"}], "td": [{"_value": "50"}, {"_value": "10"}, {"_value": "60"}]}, {"th": [{"_value": "total"}], "td": [{"_value": "115"}, {"_value": "55"}, {"_value": "170"}]}]}]}]}
Complete the table. In each row, the entries for “has cell phone” and “does not have cell phone” should have the total 100%. Round entries to the nearest percentage point.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}}, {"_attributes": {"scope": "col"}, "_value": "has cell phone"}, {"_attributes": {"scope": "col"}, "_value": "does not have cell phone"}, {"_attributes": {"scope": "col"}, "_value": "total"}]}]}], "tbody": [{"tr": [{"th": [{"_value": "10 to 12 years old"}], "td": [{"_value": "42%"}, {}, {}]}, {"th": [{"_value": "13 to 15 years old"}], "td": [{}, {}, {"_value": "100%"}]}, {"th": [{"_value": "16 to 18 years old"}], "td": [{}, {"_value": "17%"}, {}]}]}]}]}
This is still a two-way table. Instead of showing
frequency
, this table shows
relative frequency
.
Two-way tables that show relative frequencies often don’t include a “total” row at the bottom. Why?
Is there an association between age and cell phone use? How does the two-way table of relative frequencies help to illustrate this?
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
A pollster attends a rally and surveys many of the participants about whether they associate with political Party A or political Party B and whether they are for or against Proposition 3.14 going up for vote soon. The results are sorted into the table shown.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}}, {"_attributes": {"scope": "col"}, "_value": "for"}, {"_attributes": {"scope": "col"}, "_value": "against"}]}]}], "tbody": [{"tr": [{"th": [{"_value": "party A"}], "td": [{"_value": "832"}, {"_value": "165"}]}, {"th": [{"_value": "party B"}], "td": [{"_value": "80"}, {"_value": "160"}]}]}]}]}
A news station reports these results by saying, “A poll shows that about the same number of people from both parties are voting against Proposition 3.14.”
A second news station shows this graphic.
[IMG]
Are any of the news reports misleading? Explain your reasoning.
Create a headline, graphic, and short description that more accurately represents the data in the table.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students may not calculate relative frequencies correctly. Look to see if they are dividing into the total for each row, instead of some other number in the row, or the total for the entire table.
Activity Synthesis
The purpose of this discussion is to help students see the usefulness of two-way tables that display relative frequency.
Some questions for discussion:
“What does the 42% in table mean?” (42% of people 10 to 12 years old have a cell phone.)
“What is the total of the percentages in the first column? What's wrong with that answer?” (205%. It doesn't make sense since it is greater than 100%. It is combining percentages of different wholes, so it doesn't make sense to add them.)
“Did you say there was or was not an association between age and cell-phone use? Explain your reasoning.” (There is an association since the percentages for the 10 to 12 year olds is very different from the other two age groups.)
“What did the relative frequency table show you that was harder to see in the original two-way table?” (It was much easier to see the association with the percentages than the numbers. For example, the number of people without a cell phone for the older 2 age groups was the same, but the percentages were a little different.)


aligns: no