Lesson 13 | Decimal Fractions | 4th Grade Mathematics

Objective

Solve word problems involving money.

Common Core Standards

Core Standards

The core standards covered in this lesson

4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Measurement and Data

4.MD.A.2 — Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Foundational Standards

The foundational standards covered in this lesson

2.MD.C.8

Measurement and Data

2.MD.C.8 — Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Make sense of a three-act task and persevere in solving it (MP.1).
Solve word problems involving money (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

“Students…combine competencies from different domains as they solve measurement problems using all four arithmetic operations, addition, subtraction, multiplication, and division” (MD Progression, p. 20). Thus, students will solve word problems involving money recorded as decimal quantities in this lesson, connecting the supporting work of measurement problems (4.MD.2) across domains to the major work with decimals (4.NF.C) as well as the major work of solving word problems using the four operations (4.OA.3).

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Act 1: Look at the following image -

Then watch the video Piggy Bank.

a. What do you notice? What do you wonder?

b. Is there enough money to purchase the paint set? Make an estimate for how much money is in the piggy bank.

Guiding Questions

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Problem 2

Act 2: Use the following information to determine whether there is enough money in the piggy bank to buy the paint set –

There are 70 nickels in the piggy bank.
There are 64 quarters in the piggy bank.
There are 105 dimes in the piggy bank.
There are 230 pennies in the piggy bank.

Guiding Questions

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Problem 3

Act 3: See the solution below –

Was your answer reasonable? Why or why not?

Guiding Questions

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Problem 4

Act 4 (the sequel): If she buys the paint set, how much money will she have left over?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Why would Jenna give the clerk a $20 bill and a quarter in #4 rather than just a $20 bill?
How could you use rounding to find the reasonableness of your answer to #5? About how much do a pen and a calculator cost altogether? Are your answers reasonable?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Arturo needs $4 to buy candy after school. He searched the couch cushions and found 7 quarters, 3 nickels, and 21 pennies. How much more money does he need to be able to buy the candy?

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 12

Lesson Map

Topic A: Understanding Tenths

Represent decimals to tenths less than or equal to one with area models. Write a decimal value in fraction, decimal, and unit form.

4.NF.C.6

Represent decimals to tenths greater than one with pictorial base ten blocks. Write a decimal value in fraction, decimal, unit, and fraction and decimal expanded form.

4.NF.C.6

Topic B: Understanding Tenths and Hundredths

Represent decimals to hundredths less than one, understanding the equivalence of some number of tenths and ten times as many hundredths. Write a decimal value in fraction, decimal, and unit form.

4.NF.C.5 4.NF.C.6

Represent decimals to hundredths more than one. Write a decimal value in fraction, decimal, unit, and decimal and fraction expanded form for some number to hundredths.

4.NF.C.5 4.NF.C.6

Regroup decimal numbers with more than 9 tenths or 9 hundredths into simplest unit form and vice versa.

4.NF.C.5 4.NF.C.6

Topic C: Decimal Comparison

Locate decimals on a number line and explain their placement.

4.NF.C.6

Compare two decimals, recording the result of a comparison with the symbol >, =, or <, and justify the conclusion.

4.NF.C.7

Compare two or more decimals written in various forms.

4.NF.C.7

Topic D: Decimal Addition

Add tenths with hundredths written as decimal fractions.

4.NF.C.5

Add tenths with hundredths written as decimals.

4.NF.C.5

Solve word problems involving the addition of decimals and decimal fractions.

4.NF.C.5

Topic E: Money as a Decimal Amount

Find the value of some combination of dollar bills and coins.

4.MD.A.2

Solve word problems involving money.

4.MD.A.2

Decimal Fractions

Objective

Common Core Standards

Core Standards

Measurement and Data

Foundational Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem 4

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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