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Part 1 Overview Like Denominators, Connection to Base Use What You Know Bar Model and. Ten Concepts Compare Same Size Number Lines,5 tens 7 tens 3 1 1 whole. 4 4 3 1 1 1 1,3 fourths 1 fourth,3 hundreds 1 hundred 1 1 1 1 1. 1 1 1 1 4 4 4 4 4,7 ones 2 ones,I know all the units are. fourths so they are all,the same size Three 4 4 4 4 4.

fourths is greater than,Page 2 of 24 MCC WCCUSD 10 12 13. Part 1 Like Denominators, We ve been working with fractions for a while Now we are going to compare fractions. You ve already compared GREATER numbers like 100 and 1 000. Let s talk about what you already know about comparing greater numbers. You already know that 2 tens are less than 3 tens, You already know that 2 thousands are less 2 tens 3 tens. than 3 thousands,What s the same about the two sides Share with. your neighbor I need a quiet hand to share 2 thousands 3 thousands. In the first they are both tens In the second,they are both thousands.

What s different about the 2 sides Share with,your neighbor Quiet hand to share. One side has only 2 objects The other has 3, In either of the pictures are there tens on one side and thousands on the other no. You are correct That s because we have been comparing the same size units tens to tens and. thousands to thousands That can make comparing easier because all we have to do is count. the number of units on each side,Let s apply this idea to fractions. If we had 2 sixths on one side and 3 sixths, on the other which would be greater 3 sixths 2 sixths 3 sixths. Of course Use tiles and or drawing to show 1 1 1 1 1. So already we can compare some fractions without doing much work If the denominator is the. same for both fractions we know that the units or pieces are the same size Which part of the. fraction is the denominator the bottom number, Then all we have to do is compare the numerator which tells us the number of units Where is.

the numerator the number on the top,Page 3 of 24 MCC WCCUSD 10 12 13. Using Fraction Tiles As Necessary,We Do Compare and. is the denominator 4 So we are working wit fourths We have 3 fourths and 1. fourth Raise your hand if you know which is greater hands Which one 3 fourths. Good Let s write down your thinking, Possible Student Notes Students prove answers with. fraction tiles,Compare and 3 1,3 fourths 1 fourth,The check mark indicates that they have. proven their answer with fraction tiles, You Tries Have students work with partners or on their own to compare several pairs of.

fractions using the same process you just did with thems. 3rd grade denominators are 2 3 4 6 and 8 Fourth grade denominators are 2 3 4 5 6 8. 10 12 and 100 You can include 4th grade denominators in your you tries as an extension. Model Drawings and Number Lines, We Do from the day before This time make model drawings and number lines. 1 whole 1 whole 1 whole,3 1 1 1 1 3 1 1 1 1,4 4 4 4 4 4 4 4 4 4. Let s start by dividing the, whole into 2 equal pieces Included in the lesson are bar model outlines to get. Now what could we do started if needed but students should also be. drawing their own models Student drawings do not,If I divide each piece into. have to be perfect This is a chance to develop spatial. 2 would I have 4 pieces,awareness and fine motor skills.

altogether,Page 4 of 24 MCC WCCUSD 10 12 13,Number Lines. 0 1 0 1 2 3,Mark each unit in 4,Establish 0 1 and halfway. mark Then divide each fourths Plot 1 fourth,half into 2 equal pieces and 3 fourths. Student Notes,You Tries for Model Drawings and Number Lines. 3 grade denominators are 2th 3 4 6 and 8 Fourth grade denominators are 2 3 4 5 6 8. 10 12 100 You can include 4 grade denominators in your you tries as an extension. You Try and,4 5 Student Notes,4 1 1 1 1 1 1,0 1 2 3 4 5 6.

6 6 6 6 6 6 6 6 6 6 6 6 6 6,5 1 1 1 1 1 1,6 6 6 6 6 6 6. Page 5 of 24 MCC WCCUSD 10 12 13,Compare Fractions to 1 Half on a Number Line. This sets students up for using 1 half as a benchmark 0 half 1. We Do Compare and to 1 half on a number line,Use your model drawing and number line. Raise your,Decide as a class if 1 fourth is greater or. hand when I,Run pencil less than 1 half Same for 3 fourths.

along the top,get h alfway,Having them find the halfway mark can. of t he w hole across t he,1 1 1 1 1 Is 1 fourth greater than 1 half Share. 4 4 4 4 4 with your neighbor how you know Is 3,Raise your hand So 1 fourth is. when I get on the left of 1,half and 3,halfway across. fourths is on the,the number line,0 1 2 3 0 1 2 3,4 4 4 4 4 4 4 4.

Establish new number line and mark 1 3,each fraction accordingly Students can 4 4. copy the new number line in their,notebooks 0 half 1. Page 6 of 24 MCC WCCUSD 10 12 13,You Try and from previous lesson. Use student example from the previous day Students draw their own number lines on a new. page or on their work from the day before and plot 4 sixths and 5 sixths The important thing is. that the fractions are plotted on the correct side of 1 half and that they are on the correct side. of each other example 4 sixths needs to be to the left of 5 sixths and both need to be on the. right of 1 half,1 whole 4 5,1 1 1 1 1 1,6 6 6 6 6 6. 0 1 2 3 4 5 6 1,5 1 1 1 1 1 1 6 6 6 6 6 6 6,6 6 6 6 6 6 6.

Additional You Tries Show students pre drawn models and number lines Have them show on. a number line whether each fraction is less than or more than half. Page 7 of 24 MCC WCCUSD 10 12 13,Part 2 Overview Compare Unit Fractions. Connection Use What You Know Bar Model and,Ten Concepts Compare Unit Fractions Number Lines. 1 1 1 whole,1 ten 1 hundred 3 6 1 1 1,1 third 1 1 1 1 1 1 1. 6 6 6 6 6 6 6,1 thousand 1 one,I can tell from the 3 3 3 3. denominators that 1,third is a larger unit than,1 hundred 1 thousand.

1 sixth but I m not sure 0 1 2 3 4 5 6,how much larger I think 6 6 6 6 6 6 6. 1 third is greater than 1,Next Steps Grade 4 Convert to Like Denominators. 1 whole We know 1 third is greater than 1 sixth because thirds. 1 are larger units than sixths We also know that they. 1 are both less than 1 half Let s look at it another way. 1 whole 1 1,1 1 1 Start with different,size units,1 1 1 1 1 1. 6 6 6 6 6 6,1 whole Convert to same size,1 1 1 1 1 1 units. 6 6 6 6 6 6 6,1 1 1 1 1 1,6 6 6 6 6 6,Compare same size 6 6.

Page 8 of 24 MCC WCCUSD 10 12 13,Part 2 Compare Unit Fractions. So far we ve focused on comparing same size units, Now we are moving into comparing units with different sizes. Let s go back again to what you already know about comparing GREATER numbers. You already know that 1 thousand is greater than,1 thousand 1 ten. You already know that 1 hundred is greater than,What s the same about each side Share with. your neighbor what you think only one unit on 1 hundred 1 one. What s different about each side Share with,your neighbor what you think one side has a.

bigger unit,How does this relate to fractions, Sometimes we compare unit fractions like 1 third and. 1 eighth If we know which piece or unit is bigger,then it s easier for us to figure it out. Let s compare 1 third and 1 eighth Thirds and eighths 3 8. are different sizes but which is bigger 1 third 1 eighth. Raise your hand if already know which is bigger How 1 1. do you know Some kids will know from experience 3 8. but may not know how to explain it,Let s write what student name thinks Now we ll. check it with the models Done, So if we can learn which units are bigger and which are smaller then that will make it. easier to compare different fractions,Page 9 of 24 MCC WCCUSD 10 12 13.

Using Fraction Tiles,Possible Student Notes,Have students work in partners to 1 1. compare unit fractions using fraction Less than Greater than. tiles Isolate one unit fraction for,example 1 half and compare the other. unit fractions to it Then switch to a 4 2,new target unit fraction Some. students with more confidence can,predict first then prove their answers. with tiles Others can discover the 1 1,answer with the tiles In either case 8 2.

they record their work, 3rd grade denominators are 2 3 4 6 and 8 Fourth grade denominators are 2 3 4 5 6 8. 10 12 and 100 You can include 4th grade denominators in your you tries as an extension. Use the data from the student comparisons of 1 half to discover how to decide if a unit fraction. is larger or smaller than another unit fraction,Put student work on the document reader. What do you notice about 1 half What is it Possible Student Notes. greater than What is it less than Share with, your neighbor Walk around and notice Less than Greater than. student observations, Call on a student Which fractions are less than None. 1 half 1 fourth 1 sixth 1 eighth and 1 third,What is 1 half less than none Really.

Why is that Think Share with a neighbor 1 1,If a student is willing he she can share out 8 2. Let s find out 3 2,Page 10 of 24 MCC WCCUSD 10 12 13. Draw on the board We start with 1 whole,You said the biggest unit was 1 half 1 whole. How many halves in a whole 2 Okay 2 2 2,What was next largest Check with your. partner Thumbs up when you have it 1 whole,Everyone thirds How many thirds 3 Okay 3 1 1.

pieces 2 2,What s next fourths,Then what sixths,Then what eighths. I don t want you to have to watch me draw the 2 2,whole time so I m just going to add in the 1 1 1. Think why are fourths less than halves Share,with your neighbor Quiet hand because. there are more pieces in the whole Thumbs,up if you agree What if we broke the whole. into tenths or ten pieces Would the pieces be,bigger or smaller smaller What about 1 whole.

hundredths or a hundred pieces smaller 1 1, I think this is important stuff so let s put this in 4 4 4 4. notebooks Let s start with 1 whole like I,did Then divide into 2 pieces For our. notebooks we re going to skip to fourths,because that s easier to do at first Now let s go. to the smallest unit the eighths, If we extend the fourths down to the next layer 1 1. we will have 4 sections But I need 8 What 22, should I do If I divide each fourth into 2 pieces 1 1 1 1.

then will I have 8 Let s check 2 4 6 8 Yes it 1 1 1 1 1 1 1 1. works 8 8 8 8 8 8 8 8,Page 11 of 24 MCC WCCUSD 10 12 13. So we said that If there are a lot of pieces in the whole the size of one piece is small. If there are only a few pieces in the whole the size of one piece is big. Do you agree Yes of course, What part of the fraction tells us how many pieces in the whole 1 Is it here no. Is it here yes What do,4 we call that part the, That s good stuff Let s write that down in our notes. denominator, The denominator tells us the number of pieces in the whole. A greater denominator means a smaller piece,A smaller denominator means a larger piece.

Possible Student Notes,1 1 1 1 1 1 1 1,8 8 8 8 8 8 8 8. The denominator tells us the number of pieces in the whole. A greater denominator means more pieces which means smaller pieces. A smaller denominator means fewer pieces which means larger pieces. Page 12 of 24 MCC WCCUSD 10 12 13,Models Drawings and Number Lines. We Do Compare and, for a second Which piece do you think is greater Share with your neighbor Thumbs. up for 1 third Thumbs up for 1 sixth Okay, Let s look at the denominator Note the denominator for each Note the number of pieces in. Let s make a prediction It doesn t matter if you predict correctly or incorrectly as long as you. back and model checking your answer,Possible Student Notes.

Walk kids through,model drawing an,number lines as. 1 third 1 sixth,needed Notice which is,1 whole 0 1 2 3. Remind students that 1,1 1 1 3 3 3 3,both number lines need. to be the same length 1 1 1 1 1 1 1,0 1 2 3 4 5 6,they are 6 6 6 6 6 6 6. working with the same 6 6 6 6 6 6 6,Sample You Try Compare and 1 1.

1 eighth 1 fourth,2 2 4 4 4 4,1 1 1 1 1 1 1 1 0 1 2 3 4 5 6 7 8. 8 8 8 8 8 8 8 8,8 8 8 8 8 8 8 8 8,Page 13 of 24 MCC WCCUSD 10 12 13. After a few more you tries add the layer of comparing to 1 half Go back to your notes for the. We Do 1 third and 1 sixth,Student Notes,Walk kids through comparing to 1 half 1 1. Some ways to help them Use your picture 6 3,or number lines to help Also remember. that before we said that all the unit 1,fractions 1 sixth 1 eighth etc were less 2.

than 1 half Students write in their notes,Pull out the first you try 1 eighth and 1. fourth Review with the students as,needed Have them try plotting 1 eighth. and 1 fourth on the new number line,themselves 0 1. After that students can incorporate model drawings and both sets of number lines in their. Some fractions are more difficult for students to draw For example 1 third and 1 fourth It is. good to give students guidance and experience trying to draw these models There are also pre. drawn models at the end of the lesson that can be used as needed. 1 whole 1 1,0 1 2 3 4 3,3 3 3 3 3 3 3,1 1 1 1 0 1,Page 14 of 24 MCC WCCUSD 10 12 13. Part 3 Overview Unlike Denominators Like Numerators. Connection to Base Use What You Know Bar Model and. Ten Concepts Compare Same Number Lines,Number of Different.

different denominators e g by creating common denominators or numerators or by comparing to a benchmark fraction such as 1 2 Recognize that comparisons are valid only when the two fractions refer to the same whole Record the results of comparisons with symbols gt or lt and justify the conclusions e g by using a visual fraction

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