Grade 6 Math. Numeracy: Text Chapter 2

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2 Grade 6 Math Numeracy: Text Chapter 2

3 Standard Form All numbers with spaces between periods (groups of 3 starting at place value 1) Large whole numbers are arranged in groups of three digits called periods. No commas used i.e the Short Form would be 1.3 billion

4 Word Form A whole number might be spoken aloud, in its word form. Starting from the ones place at the far right, each three-digit place value group makes up a period ones, thousands, millions, billions, and so on For example, the number is read, three billion, two hundred one million, fi ve hundred thirty-six thousand, seven hundred ninety-four.

5 Place Value Chart The digits used to write a number in standard form take their proper positions in the number according to a system of writing numbers called the decimal (or base ten) system, wherein every position, or place has a corresponding and specific place value. The number and are shown as an example of how to fill in the place value chart with a specific whole number or decimal number.

6 Decimals A Decimal Number (based on the number 10) contains a Decimal Point. It is all about Place Value! As we move right of the ones place value, each position is 10 times smaller. We can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:

7 Expanded Form The expanded form of a number breaks it down and calls attention to its parts by presenting the number as the total of its digits values. For example, the expanded form of the number is 6 ten-thousands + 3 thousands + 2 hundreds + 7 tens + 9 ones or simply

8 Base Ten Diagram We can use models, diagrams, or sketches to represent a number. The Base Ten diagrams offer a simple way to represent numbers visually. For example the number can be modeled by:

9 Rounding Numbers A rounded number has about the same value as the number you start with, but it is less exact. For example, 341 rounded to the nearest hundred is 300. That is because 341 is closer in value to 300 than to 400. When rounding off to the nearest dollar, $1.89 becomes $2.00, because $1.89 is closer to $2.00 than to $1.00 Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40 If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30 4,827 rounded to the nearest ten is 4,830 but 4,827 rounded to the nearest hundred is 4,800 1,951 rounded to the nearest thousand is 2,000 (watch the ripple effect when rounding numbers to 0)

10 Exact verses Estimate In mathematics we often stress getting an exact answer. But in everyday life a few cents here or there are not going to make much difference... you should focus on the dollars! Estimation is... finding a number that is close enough to the right answer. You are not trying to get the exact right answer What you want is something that is good enough (sometimes when working with large numbers and sometimes because you are in a hurry!)

11 Estimation Strategies Pg A- C. Class discussion.

12 Show what you can do! Current world population is Write this number in a place value chart, in words, expanded form, and as a usable rounded number for conversation.

13 Show what you can do! Current world population is Write this number in a place value chart, in words, expanded form, and as a usable rounded number for conversation

14 Show what you can do! Current world population is Write this number in a place value chart, in words, expanded form, and as a usable rounded number for conversation. Seven billion, three hundred twenty three million, two hundred thirty five thousand, two hundred sixty one. 7.3 billion

15 Communication Checklist Pg 51. Discuss and Connect with expectations on work and evaluations

16 Practice and find out what you Know Chapter 2 Text Questions: pg38 #1,2,3a,5, 9; pg44 #1,3,5; pg 48 # 1,2,3,7,10; pg 53 # 1-5 Quiz on September, 2015

17 Place Value with Decimals through Millionth Starting with the ones place, let s name the places together, in order, from ones to millions: ones tens hundreds thousands ten thousands hundred thousands millions

18 Starting at the decimal point, the places are named in the same order except: there is not a ones place all names end in ths ones tens hundreds thousands ten thousands hundred thousands millions (.) decimal tenths hundredths thousandths ten thousandths hundred thousandths millionths Look at your place value chart to to see how all these titles line up together. 18

19 Standard Form Review for Whole Numbers 1. (you can use this for extra practice) 2. Write each number in standard form. (on a sheet of paper) a) 83 thousand 903 b) (9 x ) + (8 x 1 000) + (3 x 100) + (4 x 10) c) four hundred eighty-nine thousand, three hundred forty-one d) (5 x ) + (3 x 1 000) + (7 x 10) e) 48 thousand 16 f) two hundred eight g) sixty-five billion, two million, fourteen thousand, three We will check your answers in 3 minutes

20 Whole Number Practice Answers A-G 2. Write each number in standard form. a) b) c) d) e) f) 208 g)

21 How to Read and Write Decimals Write the following number in word form: Step 1: Write the word name for the #s to the left of or before the decimal point. forty Step 2 : Write and & the word name for the #s to the right of the decimal point. forty and three hundred eighteen Step 3: Write the place value name of the final digit after the decimal point. forty and three hundred eighteen thousandths

22 Practice with Decimal Numbers Try to write the following in word form. 1) )

23 Check Your Answers Try to write the following in word form. 1) seven and four thousand five ten thousandths 2) twenty-eight thousand sixty-seven hundred thousandths

24 How would you write this # in word form? th h t o. t h th 10 th 100 th m

25 Seven hundred twenty thousand, three hundred eightyfive millionths th h t o. t h th 10 th 100 th m

26 What place is the 4 in? th h t o. t h th 10 th 100 th m.

27 What place is the 4 in? th h t o. t h th 10 th 100 th m

28 What number is in the hundred thousandths place?

29 What number is in the hundred thousandths place?

30 Try to write the following number in standard form: Four and twenty-nine millionths ** Remember: when writing a decimal in standard form, start by placing the decimals in the correct place and then work backwards. Use your place value chart to help you write this number.

31 Answer Four and twenty-nine millionths the nine is in the millionths place

32 th h t o. t h th 10 th 100 th m

33 For more practice try the following website Change the level to 6 and change the answers to just decimals.

34 Practice and Find out What you Know Read to self: Topic - decimals to millionth Review pg54-5 Discuss A-D with a partner (<5min) Class discussion: estimating with millionths. How would we estimate this number ? Work with a partner to answer question on page 57 (<3min) Self Read: Review pg58-9 on using place value chart and comparing numbers. Text Questions: pg56 #2,3,4,6; pg60 #1,2,4,5, 6, 8,10. Chapter Review pg 63-4 #1-8 All questions due. Be prepared to identify those questions giving you trouble so we can review as a class. Test Date:.