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

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?

July 28, 2016
by leesclassroom
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Application For Today’s Maths Lesson: Simplifying/Equivalence

Use the Fraction Wall find, draw and write as many equivalent fractions as you can.  (Teacher will model how to draw 2 Fraction Bars under each other, the same length, showing the equivalent region by shading, labelling on the fraction bar.) 

Solving and proving solutions using models and processes for Equivalent Fractions:

  • Your family ordered two pizzas.  They ate 2/3 of the Cheese pizza and 2/6 of the Pineapple pizza.  Now mum wants to put all of the leftovers into the one box, will they fit?  Show a diagram to prove this and also show the fractions you are using.

Reasoning using knowledge of equivalence:

  • For Grandpa’s 70th birthday you buy a big chocolate cake and a big vanilla cake to have enough for the whole family.  You cut the cakes into 12ths.  Three quarters of the chocolate cake is eaten and two- thirds of the vanilla cake is eaten.  Altogether, what fraction of a cake is leftover?
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