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 multiply multi-digit whole numbers using the standard algorithm.

Answer: 
Yes. This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.

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

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im_task_000157_pos_0

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fl_problem_000674_pos_0

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standard_description: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
problem_activity: Activity
Students have learned several effective methods to divide a whole number by a whole number, including cases when there is a remainder. The goal of this task is to introduce a method for dividing a decimal number by a whole number. Students notice that the steps in the division process are the same as when dividing a whole number by a whole number, whether the division is done with base-ten diagrams, as in this task, or using partial quotients or the division algorithm as in future tasks. Here, students need to think even more carefully about place value and where the decimal point goes in the quotient.
Throughout this activity, students rely on their understanding of equivalent expressions to interpret the unbundling in Elena’s process. For example, to unbundle a one into ten tenths means going between the expressions 1 and
\(0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1+0.1\)
.
Launch
Give students 1–2 minutes of quiet think time for students to analyze Elena’s work. Pause and discuss with the whole class. Select a couple of students to share their analyses of what Elena had done to divide a decimal by a whole number. Then, give students 8–9 minutes to complete the questions and follow with a whole-class discussion.
Student Facing
To find
\(53.8 \div 4\)
using diagrams, Elena began by representing 53.8.
[IMG]
She placed 1 ten into each group, unbundled the remaining 1 ten into 10 ones, and went on distributing the units.
This diagram shows Elena’s initial placement of the units and the unbundling of 1 ten.
[IMG]
Complete the diagram by continuing the division process. How would you use the available units to make 4 equal groups?
As the units get placed into groups, show them accordingly and cross out those pieces from the bottom. If you unbundle a unit, draw the resulting pieces.
What value did you find for
\(53.8 \div 4\)
? Be prepared to explain your reasoning.
Use long division to find
\(53.8 \div 4\)
. Check your answer by multiplying it by the divisor 4.
Use long division to find
\(77.4 \div 5\)
. If you get stuck, you can draw diagrams or use another method.
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?
A distant, magical land uses jewels for their bartering system. The jewels are valued and ranked in order of their rarity. Each jewel is worth 3 times the jewel immediately below it in the ranking. The ranking is red, orange, yellow, green, blue, indigo, and violet. So a red jewel is worth 3 orange jewels, a green jewel is worth 3 blue jewels, and so on.
A group of 4 craftsmen are paid 1 of each jewel. If they split the jewels evenly amongst themselves, which jewels does each craftsman get?
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
Some students may stop dividing when they reach a remainder rather than unbundling the remainder into smaller units. Remind them that they can continue to divide the remainder by unbundling and to refer to Elena’s worked-out example or those from earlier lessons, if needed.
Activity Synthesis
Ask a student or two to display and explain their work. Ask if others performed the division the same way and if there are disagreements.
Then, focus the discussion on the connections between a division problem with a whole-number dividend (such as
\(62 \div 5\)
) and that with a decimal dividend (such as
\(53.8 \div 4\)
). Discuss:
How is the division problem
\(53.8 \div 4\)
similar to
\(62 \div 5\)
from a previous lesson?
In both problems, when we get to the final place value (tenths for
\(53.8 \div 4\)
and one for
\(62 \div 5\)
), there is still a remainder.
In both problems, to complete the division and find the quotient we need to introduce a new place value (hundredths for
\(53.8 \div 4\)
, and tenths for
\(62 \div 5\)
).
We have to unbundle at every step in both division problems.
How is the division problem
\(53.8 \div 4\)
different to
\(62 \div 5\)
from a previous lesson?
There is already a decimal in
\(53.8\)
: we had to write the decimal point for
\(62 \div 5\)
.
The quotient
\(53.8 \div 4\)
goes to the hundredths place, so there is an extra step and an additional place value.
If we were to rewrite
\(62 \div 5\)
as
\(62.0 \div 5\)
(which is what is needed in order to complete the division), then the two division problems look similar. The biggest difference between
\(53.8 \div 4\)
and
\(62 \div 5\)
is that the former problem has an answer in the hundredths while the answer to the latter only has tenths.
Representing, Speaking, Listening: MLR2 Collect and Display.
As students discuss how the division problem
\(53.8÷4\)
is related to
\(62÷5\)
from a previous lesson, create a two-column display with “similarities” and “differences” for the headers. Circulate through the groups and record student language in the appropriate column. Look for phrases such as “whole-number dividend,” “decimal dividend,” and “place value.” This will help students compare and contrast different types of division problems by recognizing the structure of the numbers.
Design Principle(s): Support sense-making; Maximize meta-awareness


aligns: no