Tenths are an Important Fraction Level 4 Module 5 Introduction to Decimal Fractions: Tenths

© Professor Pete's Classroom. All rights reserved. Index Think Bubble Mathematics: Level 4 Module 5 © Professor Pete's Classroom. All rights reserved.

Think Bubble Math: Level 4 Overview Module 1: 243731_TBM401_Mult_facts _Strategies_I.pptx Module 2: 243736_TBM402_Mult_facts _Strategies_II.pptx Module 3: 243741_TBM403_Mult_facts _Strategies_II.pptx Module 4: 241710_TBM404_Fractions _equivalent.pptx Module 5: 241801_TBM405_tenths.pptx © Professor Pete's Classroom. All rights reserved.

Think Bubble Math Worksheets: Many lessons are supported by corresponding worksheets Purchasers: Included in zip file for download Members: Access via profpete.com in TBM section Some lessons recommend that students use hands-on materials 243504_TBM102_WS_Counting_on_back_1_2_3 © Professor Pete's Classroom. All rights reserved.

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(c) Professor Pete's Classroom, 2017. All rights reserved. Tenths as Decimals ACMNA079 Recognise that the place value system can be extended to tenths... Make connections between fractions and decimal notation (c) Professor Pete's Classroom, 2017. All rights reserved.

Assumed Prior Knowledge Students should already be able to: Read and write common fractions Fold paper into fractions Divide shapes and shade parts to form common fractions Locate common fractions on a number line (c) Professor Pete's Classroom, 2017. All rights reserved.

Decimals - Tenths Decimals represented as: Common fraction of a folded sheet Parts of a shape Counting on a number line Location on a number line Base ten blocks – fraction of a one block Mixed numbers as a decimal number and its location on a number line

Accompanying worksheets for Printing Lesson 3 You will need both copies of the sheets (shown below) per student as there are eight questions Lesson 4 Only one copy of this worksheet is needed per student for this lesson Students will also need a one base ten block to place on their desks for size reference This file contains 2 copies of the required the worksheets for lesson 3 and one copy of the worksheet for lesson 4. Duplicate only once per student 241802_TBM405_tenths_WS (c) Professor Pete's Classroom, 2017. All rights reserved.

Supporting Resources: Resources at profpete.com Gadgets Interactive Software Equivalent Fractions: Lesson 7 Convert Common to Decimal Fraction Equivalent Fractions: Template C Equivalent Fractions to Hundredths and then Decimals Fraction Conversions: Common Fractions can be Written in Different Ways Fraction Conversions: Converts between Common Fractions, Decimals & Number Lines Decimals Tenths: Introduction Decimals Tenths: Number Expander Decimals Tenths: Before & After Decimals Tenths: Counting Decimals Tenths: Comparing Odometer Counting by 1: Numbers to 99.9 Odometer Counting by 2 or 5: Numbers to 99.9 Fractions Counter Gadget Fractions Converter Gadget Odometer (c) Professor Pete's Classroom, 2017. All rights reserved.

Lesson 1: Introduction to tenths ACMNA079 Recognise that the place value system can be extended to tenths... Make connections between fractions and decimal notation (c) Professor Pete's Classroom, 2017. All rights reserved.

Folding Tenths Fifths are smaller than quarters (or fourths) Find a quarter using the finger slide method along the edge of the paper. Take care with judging where the first fold should be A fifth is smaller than a quarter so move your finger slightly to the left Fold the first fifth section here Do not mark this point. Use your finger as a marker Do not mark this point. Use your finger as a marker 1 4 Give students a sheet of paper (blank on both sides) and have them find where the one quarter mark is Don’t let them mark it though, just hold the place with their finger Slide the fingers again to find one quarter One quarter is smaller than a fifth so they will need to slide their finger which way? The first time they will find it a little difficult as a judgement call is needed on how far to slide their finger. Use discretion in finding this spot. Have students mark it and fold the first fold 1 5

Folding Tenths Once the first fifth is folded, how many fifths remain to be to created? 4 x So fold the remaining piece into four pieces, fold a half… Then fold it again Open it out and you should have fifths 1 5 The remaining piece of the paper needed to be divided into four pieces to make up the four fifths Have students think of a way that this might be possible Repeat the folding to create four more sections When opened out there will be 5 pieces Discuss with students why their first section may not be as accurate as the other four sections. Are they really fifths? (not really but they are close) Allow students to practice with other sheets of paper. Can they get it more accurate? Which one of the sheets folded is the best? Discard the others and write fifths on the best one

Folding Tenths From fifths it is easy to fold tenths Fold the fifths back up again then fold it in half Open it out and there should be 10 sections Label them 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 By folding in half again the five pieces are doubled to make tenths Have students write the symbol for one tenth in each section

Writing Tenths and Decimals Tenths are a special fraction Flip the sheet over, and Write 0.1 in each of the sections 1 10 0.1 0.1 0.1 0.1 0.1 Tenths can be written in two ways – as common fractions and as decimal fractions 0.1 0.1 0.1 0.1 0.1 Tenths are a special type of fraction They are written in a different way, as decimal notation Draw students' attention to the decimal point The zero is placed at the front of a decimal to draw attention to the decimal point that can be missed as a speck on screen or paper Have students write 1/10 = 0.1 in their exercise books 1 10 = 0.1

0.3 Folding Tenths = 0.1 3 10 Flip the sheet back again Shade and write Flip the sheet again Shade three tenths then write = 0.3 3 10 1 10 0.1 Have students flip their sheet back again, shade 3/10 and write in their books 3/10 Now flip the sheet back again to the decimal side and shade three tenths. It does not need to be the exact same 3 sections Have them write 3/10 = 0.3 Encourage students to say “three tenths” rather than “zero point three” as the latter does not confer meaning. By using the name tenths, the connection to the common fraction is made. 3 10 = 0.3

Folding & Shading 10 Tenths Watch as the entire page is shaded, one tenth at a time, until all 10 tenths are shaded Watch the fractions count up one tenth at a time, all the way to The final amount shaded is 10 tenths, or one whole 0.1 0.1 0.1 0.1 0.1 10 0.1 0.1 0.1 0.1 0.1 Discuss 10 tenths making one whole (not 0.10) 10 6 5 7 8 9 4 1 2 3 = 0.9 1.0 0.8 0.1 0.7 0.3 0.5 0.6 0.4 0.2 10

0. 0.7 0. 0.2 1 Writing Tenths = = = = = a) b) c) d) e) 10 5 10 10 Complete these decimal fraction 10 5 10 b) = common fraction = c) 0. 0.2 decimal fraction 10 = d) common fraction Have students write the fractions Discuss d) and e). These make a whole number which can be written as a common fraction and as a decimal. Click to reveal the answers = 1 e) decimal fraction

0.6 0.4 0.7 0.9 1 Writing Tenths = = = = = a) b) c) d) e) 6 10 4 10 7 Complete these questions, matching each common fraction with the decimal fraction a) = 0.6 4 10 b) = 0.4 7 10 c) = 0.7 9 10 = 0.9 d) Have students write the complete number sentence fill in the answers as they go The last click will reveal the answers 10 = 1 e)

Lesson 2: counting tenths with shapes and number lines ACMNA079 Recognise that the place value system can be extended to tenths... Make connections between fractions and decimal notation (c) Professor Pete's Classroom, 2017. All rights reserved.

Counting Tenths with Shapes Count forwards Count forwards with clicks Encourage students to use the correct term of “one tenth” etc when counting 4 5 2 7 3 8 10 6 9 1 10 = 1 .0 0.8 0.3 0.2 0.1 0.4 0.5 0.9 0.7 0.6 1

Counting Tenths with Shapes Count backwards Count backwards by clicking the back arrow Encourage students to use the correct term of “one tenth” etc when counting 4 5 2 7 3 8 10 6 9 1 10 = 1 .0 0.8 0.3 0.2 0.1 0.4 0.5 0.9 0.7 0.6 1

Counting Tenths with Shapes Count forwards 5 7 4 2 1 6 3 9 8 10 10 = 1 0.8 0.4 0.3 0.2 0.1 1 .0 0.5 0.9 0.6 0.7 Count forwards with clicks Encourage students to use the correct term of “one tenth” etc when counting

Counting Tenths with Shapes Count backwards 10 4 5 3 2 7 1 9 10 6 8 = 1 0.8 0.4 0.3 0.2 0.1 1 .0 0.5 0.9 0.6 0.7 Count backwards by clicking the back arrow Encourage students to use the correct term of “one tenth” etc when counting

Counting to 1 by Tenths Count on the number line Click to progress along the line Remember to call them “one tenth” etc Count on the number line

Counting Back From 1 by Tenths Click to progress backwards along the line Remember to call them “one tenth” etc Count on the number line

Counting to 1 by Tenths Count on the number line Click to progress along the line Remember to call them “one tenth” etc Count on the number line

Counting Back From 1 by Tenths Count on the number line

Lesson 3: locating Tenths on a number line ACMNA079 Recognise that the place value system can be extended to tenths... Make connections between fractions and decimal notation (c) Professor Pete's Classroom, 2017. All rights reserved.

Tenths on Number Line Write the decimal and common fraction Locate on the number line Have students write the missing fractions and place a mark on a number line that is where they think the number is located Have a student come to the board and mark or point to where they think it is located. Click to reveal more marks on the number line. Where they close? Discuss how 0.5 is halfway to 1 0.5 5 10 0.5

Tenths on Number Line Write the decimal and common fraction Locate on the number line 0.9 9 10 0.9

Tenths on Number Line Write the decimal and common fraction Locate on the number line The next two questions require students to shade the fraction where there are no tenth markings Teacher discretion is needed in assessing the accuracy of their answers 0.1 1 10 0.1

Tenths on Number Line Shade the fraction and write the common fraction Locate on the number line 0.6 6 10 0.6

Numbers to 100 What number is at this position on the number line Write the decimal and common fractions Shade the fraction 0.8 8 10 0.8

Tenths on Number Line What number is at this position on the number line Write the decimal and common fractions Shade the fraction 0.2 2 10 0.2

Numbers to 100 Shade the fraction and write the decimal fraction Locate on the number line The next two questions require students to shade the fraction where there are no tenth markings Teacher discretion is needed in assessing the accuracy of their answers 0.4 4 10 0.4

Tenths on Number Line Shade the fraction and write the decimal fraction Locate on the number line 0.7 7 10 0.7

Lesson 4: tenths with base ten blocks ACMNA079 Recognise that the place value system can be extended to tenths... Make connections between fractions and decimal notation (c) Professor Pete's Classroom, 2017. All rights reserved.

Tenths – Base Ten Blocks This is 1 one block It is cut up into 10 pieces Each piece is one tenth 1 10 10 = 0.1 = 1 Give students 1 one block each to look at as a reference for size Click through the animation to show what happens when this block is cut up into 10 tenths Ask them to look at their block and imagine cutting it up into 10 pieces That is the size of a tenth block

Tenths – Base Ten Blocks Look at this number shown with base ten ones and tenths tenths 2. 3 decimal point Have students watch and compare the sizes of the parts of a decimal fraction

Tenths – Base Ten Blocks What number is shown here? 0. 4 4 10 = 0.4

Tenths – Base Ten Blocks What number is shown here? 2. 9

Tenths – Base Ten Blocks What number is shown here? 5. 7

Tenths – Base Ten Blocks Here are some whole ones and some tenths Write the number as a mixed number and as a decimal fraction This shows a number as whole ones and tenths Have students write it as a mixed number (whole number and common fraction) and as a decimal fraction Remember say the decimal as “two and four tenths” as this connects the two ways the number is written 3 10 2 = 2.3

Ones and Tenths – Base Ten Blocks Here are some whole ones and some tenths Write the number as a mixed number and as a decimal fraction 6 10 3 = 3.6

Ones and Tenths – Base Ten Blocks Here are some whole ones and some tenths Write the number as a mixed number and as a decimal fraction 8 10 4 = 4.8

3.5 3 3.5 Tenths on Number Line 5 10 Use the sheet provided Write the decimal and common fraction Locate on the number line 3.5 5 10 3 3.5 Hand out sheets

Tenths on Number Line Write the decimal and common fraction Locate on the number line 4.8 8 10 4 4.8

Tenths on Number Line Write the decimal and common fraction Locate on the number line 1.3 3 10 1 1.3

Tenths on Number Line Write the decimal and common fraction Locate on the number line 4.0 10 4 4.0

Tenths on Number Line Write the decimal and common fraction Locate on the number line 0.2 2 10 0.2