Decimals with a comprehensive K-5 curriculum from © E. Paul Goldenberg 2008, revised July 2011 This presentation may be shown for professional development purposes only, and may not be sold, distributed, or altered

What do students need to know? Zooming in on the number line Zooming in on the number line Arranging numbers in order Arranging numbers in order Adding and subtracting Adding and subtracting Multiplying and dividing by 10 Multiplying and dividing by 10 Multiplying decimals Multiplying decimals

Zooming in with a weak glass ½ 3

Zooming in with a weak glass

Zooming In Ten “spaces” (nine new numbers, labeled 1 to 9)

Grade 4 Student Letter

Numbers between numbers Multiply a small number by itself. Predict. Multiply a small number by itself. Predict. Square a small number (≤15). Tell me the result. I’ll “guess” your starting number. Square a small number (≤15). Tell me the result. I’ll “guess” your starting number. Let’s reverse it. Let’s reverse it. I got 36 I got 36 I got 49 I got 49 I got 43 I got 43 Hmmm… Between 6 and 7? Hmmm… Between 6 and 7?

Zooming In More Ten “spaces”Ten “spaces” (nine new numbers, labeled 1 to 9)

Zooming In… n n × n

Zooming In… n n × n

Zooming In Still More Ten “spaces”Ten “spaces” (nine new numbers, labeled 1 to 9)

Zooming In… n n × n nn × n

Zooming In… n n × n nn × n

Zooming In Even More n n × n

What do students need to know? Zooming in on the number line Zooming in on the number line Arranging numbers in order Arranging numbers in order Adding and subtracting Adding and subtracting Multiplying and dividing by 10 Multiplying and dividing by 10 Multiplying decimals Multiplying decimals

Which number is biggest? Which number is biggest? Where is the units digit? Hmm… Can’t tell yet… Where is the units digit? Hmm… Can’t tell yet… What if the others have more hidden stuff? What if the others have more hidden stuff? OK. Which is the smallest? OK. Which is the smallest? Is that it? What if there are hidden digits? Is that it? What if there are hidden digits? Sort the rest in order… What do we already know? Sort the rest in order… What do we already know? What do we know now? What do we know now? And now? And now? “Alphabetical order” to compare decimals Teach and Practice

Reading Decimals: 98.6° F Five reasons why we should not insist on pronouncing 6.53 as “six and 53 hundredths” 1. How do you write “6 53 / 100 ” as a decimal? 2. How many units? Tenths? Hundredths? / 100 sounds bigger than 6 / 10 but easy order is one of the main points of decimals 4. It’s a nuisance to pronounce Nobody, except in U.S. schools, does it.

What do students need to know? Zooming in on the number line Zooming in on the number line Arranging numbers in order Arranging numbers in order Adding and subtracting Adding and subtracting Multiplying and dividing by 10 Multiplying and dividing by 10 Multiplying decimals Multiplying decimals

Grade 4 of Think Math!

So 3.6 and 3.17 are just kinds of 3 What’s 3 + 4? Picture it on number line! What’s 3 + 4? Picture it on number line! What’s ? What’s ? What’s ? What’s ? What’s ? What’s ? What’s ? What’s ? What’s ?  What’s ? 

4 + 3 = = = = = =

43 What “tens” is it between? 4050

40 43 How far from the nearest tens?

How far is 43 from 71? –

4.3 What “ones” is it between? 45

4 4.3 How far from the nearest “ones”?

How far is 4.3 from 7.1? –

Grade 4 of Think Math!

What do students need to know? Zooming in on the number line Zooming in on the number line Arranging numbers in order Arranging numbers in order Adding and subtracting Adding and subtracting Multiplying and dividing by 10 Multiplying and dividing by 10 Multiplying decimals Multiplying decimals

Decimals & Place Value Grade 5

Why multiply and divide by 10? Practice reading numbers Practice reading numbers Reviewing place value Reviewing place value Seeing the pattern on the right side of the Seeing the pattern on the right side of the Seeing that × and ÷ by 10 undo each other Seeing that × and ÷ by 10 undo each other And… And…

What do students need to know? Zooming in on the number line Zooming in on the number line Arranging numbers in order Arranging numbers in order Adding and subtracting Adding and subtracting Multiplying and dividing by 10 Multiplying and dividing by 10 Multiplying decimals Multiplying decimals

Why multiply and divide by 10? Practice reading numbers Practice reading numbers Reviewing place value Reviewing place value Seeing the pattern on the right side of the Seeing the pattern on the right side of the Seeing that × and ÷ by 10 undo each other Seeing that × and ÷ by 10 undo each other Seeing why 28 × 32 helps with 2.8 × 3.2 Seeing why 28 × 32 helps with 2.8 × × 10 × 3.2 × 10, then divide by × 10 × 3.2 × 10, then divide by 100

TM! does decimals the way scientists, engineers, builders, mathematicians, doctors, statisticians … do. In pronunciation In pronunciation As an extension of place value As an extension of place value As an approximation As an approximation As an exact number As an exact number

Grade 4 of Think Math!

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