Neft Teacher · Notes Packet

Unit 1 · Standard 6.NS.3

Add and Subtract Decimals

Lesson 1-5

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

Illustration of Decimal: A number with a dot that shows a part between whole numbers.

3.75 means 3 ones + 7 tenths + 5 hundredths — it is between 3 and 4

Decimal

A number with a dot that shows a part between whole numbers.

Illustration of Place value: What a digit is worth based on where it sits in a number.

In 4.38: the 4 = 4 ones, the 3 = 3 tenths (0.3), the 8 = 8 hundredths (0.08)

Place value

What a digit is worth based on where it sits in a number.

Illustration of Tenths: The first spot after the decimal point. It shows parts out of 10.

0.7 = 7/10 — like 7 slices of a pizza cut into 10 equal slices

Tenths

The first spot after the decimal point. It shows parts out of 10.

Illustration of Hundredths: The second spot after the decimal point. It shows parts out of 100.

0.05 = 5/100 — like 5 pennies out of a dollar (100 pennies)

Hundredths

The second spot after the decimal point. It shows parts out of 100.

Illustration of Annex zeros: Adding zeros at the end of a decimal so numbers line up evenly.

15.7 becomes 15.70 so you can subtract 15.70 − 8.36 with aligned place values

Annex zeros

Adding zeros at the end of a decimal so numbers line up evenly.

Key Ideas & Notes

Think About It

  • What is the starting fuel amount?
  • Which operation adds fuel and which removes fuel?
  • Why is it important to line up the decimal points?

My Notes

Guided Examples

Example 1

What is 14.6 + 3.85?

Solution: Line up decimals: 14.60 + 3.85. Hundredths: 0 + 5 = 5. Tenths: 6 + 8 = 14, write 4 carry 1. Ones: 4 + 3 + 1 = 8. Tens: 1. Answer: 18.45.

Answer: A. 18.45

Example 2

What is 20.3 − 7.48?

Solution: Rewrite as 20.30 − 7.48. Annex a zero so both have two decimal places. Work carefully with borrowing: 20.30 − 7.48 = 12.82.

Answer: A. 12.82

Example 3

What is 9.05 + 4.7?

Solution: Line up decimals: 9.05 + 4.70. Hundredths: 5 + 0 = 5. Tenths: 0 + 7 = 7. Ones: 9 + 4 = 13. Answer: 13.75.

Answer: A. 13.75

Write About the Math The Writing Revolution

I can explain my steps using the words decimal, place value, tenths, hundredths, and annex zeros.

1. Kernel Sentence subject + verb

Model: Decimal is a number with a dot that shows a part between whole numbers.Decimal es un número con un punto que muestra una parte entre números enteros.

Write a kernel sentence about decimal. Use a subject and a verb.Escribe una oración base sobre decimal. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Decimal matters in mathDecimal importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Decimal matters in math because ___.Decimal importa en matemáticas porque ___.

butpero

Decimal matters in math, but ___.Decimal importa en matemáticas, pero ___.

soentonces

Decimal matters in math, so ___.Decimal importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about decimal.Di un hecho verdadero sobre decimal.

Decimal ___.

QuestionPregunta

Ask a question about decimal.Haz una pregunta sobre decimal.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about decimal.Muestra entusiasmo sobre decimal.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with decimal.Dile a un compañero qué hacer con decimal.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

I lined up the ___ so that ___.Alineé los ___ para que ___.

My answer is ___ because ___.Mi respuesta es ___ porque ___.

People use this when ___.La gente usa esto cuando ___.

Try It

Solve on your own. Check the answer key when you are done.

1. What is 50 − 23.47?

  1. 26.53
  2. 27.53
  3. 26.63
  4. 27.47
Show your work:

2. A student buys items costing $4.59, $12.75, and $3.80. What is the total cost?

  1. $21.14
  2. $20.14
  3. $21.04
  4. $21.24
Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A runner's lap times are 2.45 minutes, 2.6 minutes, and 2.38 minutes. Her personal record is 7.5 minutes total. Did she beat her record? Show all your work with decimal alignment and explain.

Sentence starter: First I lined up the decimals: 2.45 + 2.60 + 2.38 = ___. Compared to 7.50, the runner ___ beat her record because ___.

Show your work:

Reflect — Exit Ticket

What is 32.6 − 14.85?

  1. 17.75
  2. 18.75
  3. 17.85
  4. 17.25
Your answer:

Answer Key & Teacher Guide

  1. Try It 1: A. 26.53 — Rewrite 50 as 50.00. Then 50.00 − 23.47 = 26.53. You must borrow across multiple places.
  2. Try It 2: A. $21.14 — 4.59 + 12.75 + 3.80 = 21.14. Line up decimal points and add column by column.
  3. Exit Ticket: A. 17.75 — Rewrite as 32.60 − 14.85. Hundredths: 0 − 5 → borrow → 10 − 5 = 5. Tenths: 5 − 8 → borrow → 15 − 8 = 7. Ones: 1 − 4 → borrow → 11 − 4 = 7. Tens: 2 − 1 = 1. Answer: 17.75.

Writing (TWR) — what to look for