lee's classroom

(another MPPS global2.vic.edu.au weblog)

August 24, 2016
by leesclassroom
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Application For Today’s Maths Lesson: Addition and Subtraction of Fractions continued

  • Ryan was ¾ of the way through measuring the running track and he had measured 75 metres.  How long will the running track be?  (Show your thinking with a diagram and your mathematical working out.)
  • Jude wanted the class to work on their writing for ¾ of an hour.  How many minutes is that? (Prove your thinking by showing it on a clock.)
  • Griffin was asked to buy 6 metres of rope for his dad.  When his dad had used the rope to tie up the trailer, he had 50 cm leftover.  What fraction of the rope did he use? (Record using the four headings: Diagram/Table, Maths/Number, Solution Sentence, Explanation & Reasoning)
  • Mum bought 3 kg of flour to make cupcakes for Sammy’s birthday.  She used all of the flour except 200g.  What fraction of the flour was left over? (Record using the four headings: Diagram/Table, Maths/Number, Solution Sentence, Explanation & Reasoning)
  • The cyclists had completed 5/6 of the course in 42 minutes.  At this rate, how long would it take them to complete the course? (Record using the four headings: Diagram/Table, Maths/Number, Solution Sentence, Explanation & Reasoning)
  • The swimming relay team times were 1 ½ minutes, ¾ minute, 1 ¾ minutes and 2 minutes.  What was the overall time that the relay team took? (Record using the four headings: Diagram/Table, Maths/Number, Solution Sentence, Explanation & Reasoning)
  • Explain two different operations that might be used to solve the problems above.  Why do you think this is?

 

More Practice:

Group 1

Using rectangular models (see resource folder) sheet. Students cut up models as needed for subtraction.  1- 1/5, 1- 1/9, 1- 1/10, 1-5/6, 1-3/7,

2- ½, 3- 1/3, 3- 1/8
Group 2

Students are given 9/5. They are to convert this to a mixed number and record their answer.

Students are given 3 and 7/10. They are to convert this to an improper fraction and record their answer.

They are to add the two fractions together (in whatever form they prefer), recording the equation and their working out.

Why did/ didn’t you make the denominators the common?

How did you know to make all of the denominators tenths? Students simplify the answer if they have not already done so. Have students find the difference between the two fractions, recording the equation and their working out.

What does the difference mean? Why did you write this fraction first?

Have students write a word problem that includes the two fractions.   EXTEND BY changing the given improper and mixed numbers.

 

Group3

1/5 +3/10, 3/6 + 6/12, 2/9 + 1/90,

4/5 – 2/10, 5/8 – ¼, 7/9 – 1/27

August 23, 2016
by leesclassroom
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Application For Today’s Maths Lesson: Addition and Subtraction of Fractions

Practice Addition and Subtraction of Fractions – you may use a Fraction Wall or draw fraction diagrams to support your process.

1/2 + 1/4 =                    1/3 + 1/6 =                             3/4 + 1/8 =                         2/5 + 3/10 =                             1/2 + 3/8 =

1/2 – 1/4 =                     1/3 – 1/6 =                             1/4 – 1/8 =                          1/5 – 1/10                                1/2 – 1/8 =

 

1/3 + 1/7 =                 5/8 + 2/5 =                  1/3 + 3/10 =                     3/8 + 1/3  =                       3/5+ 5/9  =

1/3 – 1/7 =                7/8 – 2/5 =                   1/3 – 3/10                        3/8 – 1/3 =                       3/5 – 5/9 =

 

2 ⅓ + 3 ⅓ =                2 ¼ + 1 ½ =                   1⅖ + 4 ¾ =                        2 ⅖ + 1 ⅜=                        7 ⅔+ 4 ⅙=

5 ⅓ – 2  ⅓ =               3 ¼ – 2 ½ =                    5 ⅞- 3 ¼ =                         8 ⅖ – 6 ½ =                        9 – 3 ⅙=

 

Who needs to add and subtract fractions in real life situations?  Can you write a problem for another to solve that shows how we need to use fractions in work or at home?

 

Partners switch problems, solve and discuss.  Is the problem one that would occur in real life?  Do you and your partner agree on the solution?

August 18, 2016
by leesclassroom
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Application For Today’s Maths Lesson: Lowest Common Denominator

Group 1: using fraction wall find as many equivalent fractions of the following: ½, 1/3, ¼, 1/5, ¾, 2/5, 2/8,

Use your answers to create equations with SIMILAR fractions that you can solve:

½ + ¼=        1/3 + 4/6=    1/5 + 3/10=      ¾ + 1/8=     2/5+ 4/10=    2/8 + 1/4=      3/4 – ¼=    ¾- 2/8=    5/10 – 1/5=

Can you make your own equations using what you have learned?

 

Group 2

Find a common denominator of these to turn them into SIMILAR FRACTIONS/ then add the two fractions (remember to simplify at the end…you may need to turn improper fractions back to mixed numbers!):

1/10 and ¼

1/10 and 4/5

1/6 and 1/12

¼ and 1/12

½ and 1/10

1/8 and ¼,

2/3 and 5/6

2/3 and 8/9

1/7 and 3/14

¾ and 5/6

5/6 and 7/12

 

¾ and 5/6

7/9 and 5/6

3/8 and 2/5

2/7 and ¾

4/5 and 3/7

3/10 and 3/8

 

Grp 3:  NEW INFO

We can avoid the need to simplify at the end by finding  the lowest common multiple of the denominators.

The lowest common denominator of the denominators is the lowest common multiple of the denominators, e.g. 1/10+1/4.

The denominators are 10 and 4. Find the lowest common multiple of 10 and 4.

To find this – use your times tables/skip counting patterns for each until you find a number that is in both:

e.g:

4,8,12,16,20, 24, 28

10, 20,30, 40, 50

So 20 is the lowest common denominator

Find  LCD for these then add the two fractions (remember to simplify at the end…you may need to turn improper fractions back to mixed numbers!):

7/10 and ¼

2/3 and 4/5

5/8 and 1/12

¼ and 7/12

4/6 and 3/18

1/8 and 4/16,

2/3 and 5/6

2/3 and 8/9

1/3 and 3/15

¾ and 5/6

5/6 and 7/12

7/9 and 5/6

3/8 and 2/5

2/6 and ¾

4/5 and 3/7

3/6 and 3/8

Frameworks Year 6: chapter 7 page 161 Activity 6 including the worded problems and the Puzzles

August 3, 2016
by leesclassroom
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Today’s Maths Application: Lowest Common Denominator

How many ways to make 1?  Use the Make a Whole game, record the number sentences each time you make a whole/1.

Mum baked 2 pies and took them to grandma’s house for Sunday dinner. On Monday mum is looking at the leftovers and she wants to know if she has enough pie for the family for dinner.  She has 2/3 of one pie and 1/6 of one pie and she has 5 people to feed.  Will she have enough for each person to have one piece of pie?  Draw a diagram to show how you know, write the number sentence to show your steps to finding your solution.

You buy a block of chocolate that has 24 squares.  The first day you eat half of the chocolate.  Each day after that you eat half of what is left.  Show as a diagram and with number sentences what happens.  Explain what you notice.

Mum baked 4 pies and took them to grandma’s house for Sunday dinner. The family ate 3/8 of the beef pie, 1/3 of the steak and kidney pie, 5/6 of the cottage pie and ¾ of the curry pie.  How much is left over?   Draw a diagram to show how you know, write the number sentence to show your steps to finding your solution.  Explain your process and justify your solution.

You buy a block of chocolate that has 36 squares.  The first day you eat half of the chocolate.  Each day after that you eat half of what is left.  Show and describe what happens.  How many days will it take you to finish the chocolate and how can you justify your reasoning?

If your family drinks 1 ½ litres of milk on Monday, 1 ¾ litres of milk on Tuesday, 2 ⅔ litres on Wednesday, ⅞ of a litre on Thursday, 1 ½ litres on Friday and 3 ⅓ litres over the weekend, how many litres will they buy for the week and how much will there be left on Sunday night?

August 1, 2016
by leesclassroom
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Application For Today’s Maths Lesson: Simplifing Fractions

How many ways to make One?  Using the fraction wall, make as many number sentences as possible showing how to make one.  (students start by writing the repeated fraction, they will be encouraged to see that fractions added to related fractions also make one

e.g. ½ + ½ = 1  and ½ + ¼ + ¼ = 1 and ½ + 2/4 = 1

 

Teacher Group – Check student knowledge of equivalent fractions and simplifying, using common factors.

Sue baked an apple pie.  For dessert her family ate 3/8 of the pie, the next day they ate another 3/8 of the original pie.  What fraction of the total pie has been eaten and how much does is left?  Show this as a diagram, showing your work as equations.  Consider if the leftover amount is expressed in SIMPLEST form.  How do you know?

Grandpa bakes his famous lasagne in a big rectangular tray.  He cuts it into 18 slices and 2/3 get eaten.  How many slices were eaten and will there be enough for grandpa to give to the next door neighbours who have a family of 5?

 

The year 7 teacher will ask you to keep track of your test scores in maths.  In the first test you get 45/50, the next test 75/80, the next test 24/35, the next test 20/40 and the last test 75/100.  Put your test scores in order from least to most.  How can you prove to a friend that you are correct?

Students solve the problem and write a written explanation to prove their thinking.

Students share with a partner or in a small group to consider what is similar or different to their own thinking. 

Do all group members agree?  How will show your group members your method so that they can learn from you?

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