Junior Exams

Our Year 9's did their very first high school exam on Tuesday, 19 June starting with mathematics.

I tried to create a rich task with a meaningful context covering the Number, Measurement and Probability strands of the NZ curriculum so that learners would actively engage with the context and also to set them up for contextual learning when they reach the senior school and do NCEA exams as we have moved away from teaching skills in isolation. Not only did learners have to show detailed evidence as to how they solved questions but they also had to search online to complement already-existing content; that encouraged active interaction with the task.



Our context was about Steven Adams gifting them 4 tickets to the NZ Breakers basketball game at Spark Arena. Measurement skills included
checking online for train times and fares
converting scale diagram measurements of the basketball court
finding perimeter and area of parts of the basketball court
finding costs of the train fare if discounts were given on the day (a good way to integrate between maths strands as this was evidence of Number)

Carls Junior and Sky City Hotel are sponsors of the NZ Breakers basketball team so we used the former context for our Probability strand where learners had to look online for menus and then find the probability of certain Carls Junior combinations and the latter context was used for the Number strand. Learners had to check online for hotel and dinner prices for them, a friend and 2 adults and then work out the total cost of the prize that they had won in NZ dollars. We incorporated ratio by having them convert the total cost from NZ dollars into US dollars as Steven Adams is based in the States and is paid in that currency.

I noticed these comment from 2 of my learner's exam papers....

Thank you Mrs Dunn for creating this awesome Exam paper for us!! it was really fun. Sorry if i got some questions wrong . :)

This test was difficult, I now know what to focus on and will try harder next time

I used the HIGHLIGHT feature on teacher dashboard to see if learners were on task and the DRAFTBACK feature from the chrome webstore to see how long learners were engaged during the 2-hour exam slot and the context certainly kept learners engaged.

Differentiation and Managing Self in junior maths

While giving learners feedback on a contextual Number task, I noticed that they were struggling with fractions when denominators were different. After using an online resource, a few learners were given an opportunity to conference/collaborate in order to build up their confidence with this L4 learning while others who understood the video moved onto another activity.

For the first time in ages, all students were super-confident with L3 (adding fractions when denominators are the same). For those who needed more confidence with adding Fractions with different denominators (L4) we came up with a strategy


Level 4 strategy (adding fractions with different denominators)
1/4 + 2/5
look at your 2 denominators - by this stage, all learners had used the "Word definition" literacy strategy to familarise themselves with these subject-specific terms)
the 2 denominators were  (4 and 5)
count in 4's (4, 8, 12, 16, 20)
count in 5's (5, 10, 15, 20)
which number is lowest and common to both (20)
that becomes your new denominator

Learners had to figure out their new numerators in order to solve.
(multiply the first numerator by 5 and second numerator by 4) to get
5/20 + 8/20
13/20

All 4 Key Competencies (KC's) from the NZ curriculum:
Thinking
Relating to others
Using Language, symbols and text
Managing self
Participating and contributing
were incorporated into the lesson.

We also trialled the multiplication method where you cross multiply but almost all learners chose the method explained above as it automatically gave a simplified fraction as the final answer.

With this new-found confidence, learners revisited the contextual task, used the "Chunking" literacy strategy where they had to break up the context into "bite-sized" or smaller pieces were pleased with their ability to solve the problem.

Literacy in maths

To sell the importance of literacy in maths, my students and I took a mock trip to China.

Once we landed in China, we discussed taking a shuttle or taxi to our hotel and realised that none of us could speak or read Chinese. This led to a healthy discussion about the importance of knowing the language, so getting learners to define terms like:
Transformations
Complementary angles
Supplementary angles
Invariant points
Types of angles
Polygons
Bearings, to name a few, had learners attempting to understand the language of Geometry with renewed vigour. To reinforce learning, learners explained the meaning of Geometry words and then copied and pasted an appropriate image. Their final challenge was to explain at least one of the words to their neighbour and vice versa.

Straight line

Our Junior students are learning about straight equations so after using a few online interactive resources,  playing kahoot and completing a teacher-created Quizizz resource a few were still struggling to identify the gradient, also known as the slope or m value and the Y intercept or c value.

I had a conference lesson with 3 students and tried to break it down
s........l.....o.....w..........l.......y. using this example

y = 2x - 3

Teacher: Read this straight line equation
Student: y equals 2x minus 3

Teacher: Repeat it to your friend
Student: y equals 2x minus 3

Teacher: So to find the gradient you must look to see what is in front of the letter x. So what do you see in front of the letter x
Student: (silent)

Teacher: Remember to look  to see what is in front of the letter x
Student: Which way is the front?

This was a teachable moment .........................

Lesson Sequence

Number	Fractions: addition and subtraction	Year 9
Teacher practice Constructivist Experiential Differentiation	Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they can do critical thinking and show creativity as they learn (4 C’s for today’s Learners)
Learning Outcomes	Level 3: Use a range of additive and simple multiplicative strategies on fractions Level 4: Understand equivalent fractions and addition and subtraction of fractions
Success criteria Learners are successful if they can do basic addition and subtraction with fractions and simplify where necessary SOLO Taxonomy Pre structural Uni structural Multi structural Relational Extended abstract I need help I can Identify numerators and denominators I can describe a procedure and do calculations with Number problems in context I can explain and organise my thinking to solve Number problems in context I can create and predict solutions and reflect on my answers
Do Now (Introduction)	Write down 4 numbers, each with 1 decimal place. 0.1   0.4   0.3   0.6 Add the first two decimals together 0.1 + 0.4    = 0.5 Now add the last two decimals together 0.3 + 0.6     = 0.9 Write down 2 numbers with 2 decimal places. The bigger decimal should be written first. Now subtract them. 0.42 - 0.30   = 0.12 Read all three answers to your neighbour (this is to reinforce a previous lesson on place value with decimals) Write each of your Decimals above as Fractions and solve 1/10 + 4/10  = 5/10 3/10 + 6/10   = 9/10 42/100 - 30/100   121/00 What did you notice? 0.5 is the same as 5/10: we added the numerators, but kept the denominators the same 0.9 is the same as 9/10:  we added the numerators, but kept the denominators the same 0.12 is the same as 12/100 : we subtracted the numerators, but kept the denominators the same Can we make a general rule when adding or subtracting fractions? When fractions have the same denominator, we do 2 things: Firstly we add or subtract the numerators and secondly, we keep the denominator the same (level 3) So what do you think happens when the denominators are DIFFERENT? Do you think we could change the rules and add the denominators? Learners explore addition of fractions when denominators are not the same Teacher’s example can be used if learners need assistance and cannot self manage 1/3   +    2/6 Learners can use these  resource 1  and resource 2 to help them understand equivalent fractions Contextual Class challenge Tau eats ⅕ of a whole fish and Tia eats two thirds. How much of the fish is left? Teacher provocation Pick out the WHITE hat (important information) - Tau eats ⅕ and Tia eats ⅔ So what do we need to find if we use this information? How much fish was eaten What mathematical knowledge do we need in order to solve this? Addition of fractions when denominators are different. What do we need to do to solve the contextual challenge? Find out how much fish was left How do we do that? Subtract What word in the challenge gives you a hint to subtract? The word left
Lesson sequence	Adding and subtracting basic Decimals (up to 2 decimal places) Rewriting those Decimals as Fractions and solving Comparing decimal answers with fraction answers Exploring equivalent fractions Inquiring into learning using online resources Making learning visible by creating personalised notes by inserting images and explaining them and documenting evidence of learners’ understanding of basic addition and subtraction of fractions
Learning Experiences	Relating fractions to decimals Exploring equivalent fractions Developing and using strategies for adding and subtracting fractions
Resources	Google document Teacher’s Google Number  site
Literacy strategy	Word definition: Learners define unfamiliar terms Word My definition Online definition equivalent equal equal in value or amount
Sharing learning	Teacher comments on personalised learners docs and their blogs	Learners blog their learning experience and comment on peers blogs
Next steps	Curriculum Multiplication and division of fractions	Daily life If you have a recipe for your favourite treat, but wish to make a smaller amount you will need to know how to reduce the quantities of all ingredients accordingly.
Reflection	The majority of the learners already knew how to add and subtract fractions with the same denominator, so they moved on to fractions with different denominators almost immediately

Resource attribution

mathplayground.com

nteractivestuff.org

Number	Fractions: Multiplication and Division	Year 9
Teacher practice Constructivist Experiential Differentiation	Teacher conferenced with various groups using learner knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they can do critical thinking and show creativity as they learn (4 C’s for today’s learners)
Learning Outcomes	Level 4: Understand equivalent fractions Level 5: Understand operations on fractions (Multiplication and Division)
Success criteria Learners are successful if they can do basic multiplication and division of fractions and simplify where necessary SOLO Taxonomy Pre structural Uni structural Multi structural Relational Extended abstract I need help I can Identify numerators and denominators I can describe a procedure and do calculations with fraction problems in context I can explain and organise my thinking to solve fraction problems in context I can create and predict solutions and reflect on my answers
Do Now (Introduction)	Solve by using numbers and mathematical symbols half of ten        ½ x 10 = 5 one quarter of twelve     ¼ x 12 =3 one fifth of twenty        ⅕ x 20 = 4 Can you explain your thinking for each answer? ten divided by two or 10/2 = 5 twelve divided by four or  12/4 = 3 twenty divided by five or 20/5 = 4 How can you write the number 12 as a fraction Learners discuss or check online until they come up with a solution of 121 Explain three quarters of 12, but rewrite 12 as a fraction 3/4 x 12/1 3 x 12 divided by 4  x 1 = 36/4 = 9 Can we make a general rule when multiplying fractions? Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction Learners who immediately simplify 36/4 as 9 explain to their neighbour as to why they simplified the fraction Find a Google image that reinforces your knowledge of multiplying fractions and explain your learning to your neighbour. Teacher provocation Reread your general rule for multiplying fractions. Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction Using this knowledge, can we say that when dividing fractions we divide the numerators to get the top part of the fraction and divide the denominators to get the bottom part of the fraction? Learners guess either yes or no and are given time to explore online for the rules when dividing fractions before an example is discussed When dividing fractions, we go to KFC Keep, Flip, Change KEEP first fraction FLIP the fraction to the right of the division sign CHANGE division to multiplication Then use your rule “Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction” Example 2/7  ÷   3/4 becomes Answer 2 x 4      =  8             7 x 3         21 An additional challenge was done using 3 fractions to reinforce the learning that we Keep the first fraction, Flip the fractions to the right of the division sign and then Change division to multiplication Contextual challenge (card resource) Mrs Dunn is creating a cut-out resource made from special paper. She has ⅔ of a page left and needs ⅙ of a page for each resource. How many cut-out resources can she make? ⅔   ÷  ⅙ ⅔  x 6 12/3 4 cut-outs
Lesson sequence	Solving fraction x whole number Solving fraction x fraction Creating a rule when multiplying fractions Exploring division of fractions Division in context Making learning visible and documenting evidence of learners’ understanding of multiplication and division of fractions by creating personalised notes, inserting images and explaining them to peers
Learning Experiences	Relating fractions to decimals Exploring equivalent fractions Developing and using strategies for multiplication and division of fractions
Resources	Google document Teacher’s Google Number  site
Sharing learning	Teacher comments on personalised learners docs and their blogs	Learners blog their learning experience and comment on peers blogs
Next steps	Curriculum Fraction, Decimal, Percent conversion	Daily life Maximising discounts advertised as fraction and/or percent
Reflection	Remembering KFC (Keep, Flip, Change) when dividing fractions evoked much enthusiasm and discussion amongst learners

Number

Fractions: addition and subtraction

Year 9

Teacher practice

Constructivist

Experiential

Differentiation

Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they can do critical thinking and show creativity as they learn (4 C’s for today’s Learners)

Learning Outcomes

Level 3: Use a range of additive and simple multiplicative strategies on fractions

Level 4: Understand equivalent fractions and addition and subtraction of fractions

Success criteria

Learners are successful if they can do basic addition and subtraction with fractions and simplify where necessary

SOLO Taxonomy

Pre structural	Uni structural	Multi structural	Relational	Extended abstract
I need help	I can Identify numerators and denominators	I can describe a procedure and do calculations with Number problems in context	I can explain and organise my thinking to solve Number problems in context	I can create and predict solutions and reflect on my answers

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify

numerators and denominators

I can describe a procedure and do calculations with Number problems in context

I can explain and

organise my thinking to solve Number problems in

context

I can create and predict solutions and reflect on

my answers

Do Now (Introduction)

Write down 4 numbers, each with 1 decimal place.

0.1   0.4   0.3   0.6

Add the first two decimals together

0.1 + 0.4    = 0.5

Now add the last two decimals together

0.3 + 0.6     = 0.9

Write down 2 numbers with 2 decimal places. The bigger decimal should be written first. Now subtract them.

0.42 - 0.30   = 0.12

Read all three answers to your neighbour (this is to reinforce a previous lesson on place value with decimals)

Write each of your Decimals above as Fractions and solve

1/10 + 4/10  = 5/10

3/10 + 6/10   = 9/10

42/100 - 30/100   121/00

What did you notice?

0.5 is the same as 5/10: we added the numerators, but kept the denominators the same

0.9 is the same as 9/10:  we added the numerators, but kept the denominators the same

0.12 is the same as 12/100 : we subtracted the numerators, but kept the denominators the same

Can we make a general rule when adding or subtracting fractions?

When fractions have the same denominator, we do 2 things: Firstly we add or subtract the numerators and secondly, we keep the denominator the same (level 3)

So what do you think happens when the denominators are DIFFERENT?

Do you think we could change the rules and add the denominators?

Learners explore addition of fractions when denominators are not the same

Teacher’s example can be used if learners need assistance and cannot self manage

1/3   +    2/6

Learners can use these  resource 1  and resource 2 to help them understand equivalent fractions

Contextual Class challenge

Tau eats ⅕ of a whole fish and Tia eats two thirds. How much of the fish is left?

Teacher provocation

Pick out the WHITE hat (important information) - Tau eats ⅕ and Tia eats ⅔

So what do we need to find if we use this information? How much fish was eaten

What mathematical knowledge do we need in order to solve this? Addition of fractions when denominators are different.

What do we need to do to solve the contextual challenge? Find out how much fish was left

How do we do that? Subtract

What word in the challenge gives you a hint to subtract? The word left

Lesson sequence

Adding and subtracting basic Decimals (up to 2 decimal places)

Rewriting those Decimals as Fractions and solving

Comparing decimal answers with fraction answers

Exploring equivalent fractions

Inquiring into learning using online resources

Making learning visible by creating personalised notes by inserting images and explaining them and documenting evidence of learners’ understanding of basic addition and subtraction of fractions

Learning Experiences

Relating fractions to decimals

Exploring equivalent fractions

Developing and using strategies for adding and subtracting fractions

Resources

Google document

Teacher’s Google Number  site

Literacy strategy

Word definition: Learners define unfamiliar terms

Word	My definition	Online definition
equivalent	equal	equal in value or amount

Word

My definition

Online definition

equivalent

equal

equal in value or amount

Sharing learning

Teacher comments on personalised learners docs and their blogs

Learners blog their learning experience and comment on peers blogs

Next steps

Curriculum

Multiplication and division of fractions

Daily life

If you have a recipe for your favourite treat, but wish to make a smaller amount you will need to know how to reduce the quantities of all ingredients accordingly.

Reflection

The majority of the learners already knew how to add and subtract fractions with the same denominator, so they moved on to fractions with different denominators almost immediately

Number

Fractions: Multiplication

and Division

Year 9

Teacher practice

Constructivist

Experiential

Differentiation

Teacher conferenced with various groups using learner knowledge as a guide and answered all

questions by probing and encouraging learners to communicate their thinking collaboratively

so that they can do critical thinking and show creativity as they learn (4 C’s for today’s

learners)

Learning Outcomes

Level 4: Understand equivalent fractions

Level 5: Understand operations on fractions (Multiplication and Division)

Success criteria

Learners are successful if they can do basic multiplication and division of fractions and simplify where necessary

SOLO Taxonomy

Pre structural	Uni structural	Multi structural	Relational	Extended abstract
I need help	I can Identify numerators and denominators	I can describe a procedure and do calculations with fraction problems in context	I can explain and organise my thinking to solve fraction problems in context	I can create and predict solutions and reflect on my answers

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify

numerators and denominators

I can describe a procedure and do calculations with fraction problems in context

I can explain and organise my thinking to solve fraction problems in context

I can create and predict solutions and reflect on my answers

Do Now (Introduction)

Solve by using numbers and mathematical symbols

half of ten        ½ x 10 = 5

one quarter of twelve     ¼ x 12 =3

one fifth of twenty        ⅕ x 20 = 4

Can you explain your thinking for each answer?

ten divided by two or 10/2 = 5

twelve divided by four or  12/4 = 3

twenty divided by five or 20/5 = 4

How can you write the number 12 as a fraction

Learners discuss or check online until they come up with a solution of

121

Explain three quarters of 12, but rewrite 12 as a fraction

3/4 x 12/1

3 x 12 divided by 4  x 1 = 36/4 = 9

Can we make a general rule when multiplying fractions?

Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction

Learners who immediately simplify 36/4 as 9 explain to their neighbour as to why they simplified the fraction

Find a Google image that reinforces your knowledge of multiplying fractions and explain

your learning to your neighbour.

Teacher provocation

Reread your general rule for multiplying fractions.

Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction

Using this knowledge, can we say that when dividing fractions we divide the numerators to get the top part of the fraction and divide the denominators to get the bottom part of the fraction?

Learners guess either yes or no and are given time to explore online for the rules when dividing

fractions before an example is discussed

When dividing fractions, we go to KFC Keep, Flip, Change

KEEP first fraction

FLIP the fraction to the right of the division sign

CHANGE division to multiplication

Then use your rule “Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction”

Example

2/7  ÷   3/4 becomes

Answer 2 x 4      =  8

            7 x 3         21

An additional challenge was done using 3 fractions to reinforce the learning that we Keep the first fraction, Flip the fractions to the right of the division sign and then Change division to multiplication

Contextual challenge (card resource)

Mrs Dunn is creating a cut-out resource made from special paper. She has ⅔ of a page left and needs ⅙ of a page for each resource. How many cut-out resources can she make?

⅔   ÷  ⅙

⅔  x 6

12/3

4 cut-outs

Lesson sequence

Solving fraction x whole number

Solving fraction x fraction

Creating a rule when multiplying fractions

Exploring division of fractions

Division in context

Making learning visible and documenting evidence of learners’ understanding of multiplication and division of fractions by creating personalised notes, inserting images and explaining them to peers

Learning Experiences

Relating fractions to decimals

Exploring equivalent fractions

Developing and using strategies for multiplication and division of fractions

Resources

Google document

Teacher’s Google Number  site

Sharing learning

Teacher comments on personalised learners docs and their blogs

Learners blog their learning experience and comment on peers blogs

Next steps

Curriculum

Fraction, Decimal, Percent conversion

Daily life

Maximising discounts advertised as fraction and/or

percent

Reflection

Remembering KFC (Keep, Flip, Change) when dividing fractions evoked

much enthusiasm and discussion amongst learners

Number	Decimals	Year 9
Teacher practice Constructivist Experiential Collaboration	Teacher conferenced with various groups using learners knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they could do critical thinking and show creativity as they learned (4 C’s for today’s Learners)
Learning Outcomes	Level 3: Ordering decimals Level 4: Decimals and place value to 3 places Level 5: Recurring decimals (extension)
Success criteria: Learners are successful if they can order decimals, read decimals correctly, compare decimals and write decimals as percentages SOLO Taxonomy Pre structural Uni structural Multi structural Relational Extended abstract I need help I can Identify Decimals in daily life I can describe a procedure and do calculations with Number problems in context I can explain and organise my thinking to solve Number problems in context I can create and predict solutions and reflect on my answers
Do Now (Introduction)	Rearrange these letters “a decimal point” to explain what a decimal is. Use each letter only once and use all letters. Teacher reads the instruction aloud and answers any questions posed by learners Learners work independently and/or collaboratively as they work towards a possible solution I’m a dot in place
Lesson sequence	Rearrange given letters to better understand what a decimal point is If I gave you $500 would you be happy? Now along comes the decimal point and lands just after the number 5 to make $5.00, would you still be happy? Class discussion about the impact of the decimal point on the value of the money Answer question 1 and 2 to determine learners’ curriculum level Question 1. Four friends, Mele, Tui, Tevita and Anna can jump 3.1m, 3.15, 3.01 and 3.10m respectively. Arrange these distances in ascending order Teacher comment: When rearranging or comparing, decimals, look at the first digit, of each number: if they are similar, then look at and compare the next digit eg in 3.15 and 3.01 (1/10 is greater than 0/10 or 15/100 is greater than 1/100), so 3.15 is greater than 3.01 Thinking/discussion: When comparing 3.1 and 3.10 both can be read as having 1/10, so the two decimals are equal. Any zero after the decimal point that is not followed by another number is just a place-holder Question 2. Draw a number line (any length) from 0 to 1. Mark the middle and give it a decimal value. Keep finding the middle until you reach 3 decimal places. Use your learning outcomes table, from Mrs Dunn Maths site to determine the curriculum level for each Question (this is for learners to identify their learning needs) Teacher provocations How would you read this decimal 1.25? one and twenty- five hundredths one and two tenths and five hundredths one point two five not one point twenty five - Learners work independently and/or collaboratively Discuss how to read and compare decimals Explore learning using online resources Make learning visible by creating personalised notes documenting evidence of learners’ understanding of Decimals Teacher provides opportunities for learners to develop and demonstrate their thinking by discussing with peers and documenting on a Google doc. Teacher expectation is that of learners’ managing their learning. Learners self-manage by choosing the appropriate curriculum levels for the topic and can move on to the next level if they feel confident in their ability Learners show evidence of their thinking and learning by creating personalised notes after navigating the hyperlinked Decimals resources on Mrs Dunn Maths site All evidence of thinking/learning is visible on a Google document which is shared with the teacher and can also be shared with peers for commenting
Learning Experiences	Learners work independently and/or collaboratively. Writing decimals in words and symbols as learners often confuse decimals with money and read it incorrectly. Learners work independently and/or collaboratively. Comparing decimals on number lines to see progressions from smallest to biggest Learners work independently and/or collaboratively. Understanding decimals as percentages eg 0.25 is 25%
Resources	Smartboard or cut-outs of letters (so that learners can drag or rearrange letters) Google document Teacher’s Google Number  site
Literacy strategy	Word definition: Learners define unfamiliar terms Word My definition Online definition ascending going up go up or climb
Sharing learning	Teacher comments on personalised learners docs and their blogs	Learners blog their learning experience and comment on peers blogs
Next steps	Curriculum Convert common Decimals up to 2 dp) to Fractions (L3) which will lead on to basic operations with fractions (L4,5 )	Daily life Fractions are used in baking or cooking. Basic operations are used eg if ¼ cup of sugar, sometimes it is necessary to either double or halve the recipe.
Reflection	More emphasis needs to be placed on place value, particularly for numbers after the decimal point so that learners use words like tenths, hundredths and thousandths confidently. Using money as an example when learning about decimals is contradictory as $5.70 (five dollars seventy) is not read as five point seven zero dollars. There are no tens, hundreds and thousands after the decimal point; instead it is tenths, hundredths and thousandths

Number	Fraction, Decimal, Percent Conversion	Year 9
Teacher practice Constructivist Experiential Differentiation	Teacher conferenced with various groups using learner knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they can do critical thinking and show creativity as they learn (4 C’s for today’s learners)
Learning Outcomes	Level 3: Know fractions and percentages in everyday use Level 4: Know the equivalent decimal and percentage forms for everyday fractions. Level 5: Know commonly used fraction, decimal, and percentage conversions
Success criteria Learners are successful if they can convert commonly used Fraction, Decimal and Percent and can work out prices regardless of whether discounts are expressed as Fractions or Percentages SOLO Taxonomy Pre structural Uni structural Multi structural Relational Extended abstract I need help I can Identify Fractions, Decimals and Percent I can describe a procedure and do calculations with Number problems in context I can explain and organise my thinking to solve Number problems in context I can create and predict solutions and reflect on my answers
Do Now (Introduction)	On weekends or after school, where do you see Fractions and/or Percent? Online activity A few volunteers explain what they wrote on the lino board while the rest of the class listens attentively and respectfully
Lesson sequence	Question 1. Retailers express some of their discounts as Fractions and others as a Percent. Explain how to determine which discount will benefit you the most? Briscoes is offering a 25% discount on a  $20 fan and The Warehouse is one third discount on a $30 fan. Which retailer is offering you a better buy and how much change will you get if you pay with a $50 note. Statement Working Answer Briscoes discount 25% x $20 $5 Cost at Briscoes $20 - $5 $15 Change at Briscoes $50 - $15 $35 Warehouse discount ⅓ x $30 $10 Cost at Warehouse $30 - $10 $20 Change (Warehouse) $50 - $20 $30 ⅓ is bigger than 25% (¼) so Better deal is at The Warehouse Activity 1 *Screenshot a house on the internet that you would like to buy. a) How much is the house? b) Write this amount in words. (Level 3) c) What will the ⅕ deposit be? (Level 4) d) How much will still be owing? (Level 3) Real estate commission in Auckland ranges from 2.95 - 4% for the first $300 000 and then 2 - 2.5% thereafter. A base fee up to $500 is charged regardless of whether the house is sold or not. GST is also added. e)How much commission would be made if you sold your house at the price mentioned in (a) (level 5)
Learning Experiences	Learners work independently and/or collaboratively by adding their contribution to the lino activity about where they see Fractions and/or Percent. Learners work independently and/or collaboratively comparing fraction and percent Learners work independently and/or collaboratively understanding and solving discount, deposit and commission questions Talking about percentages in everyday contexts Maximising discounts expressed as Fractions and/or Percent Converting Fraction, Decimal, Percent Encouraging creativity as learners explore and select an image of a house online Using a calculator with confidence
Resources	Lino Flyers Junkmail Online retail sites Google document Mrs Dunn maths Google site - Fraction, Decimal, Percent
Literacy strategy	Chunking - break information up into smaller pieces or chunks to facilitate understanding Word definition Word My definition Online definition discount less deduction from the usual cost of something percent 100 one part in every hundred commission don’t know money paid upon completion of a task retailer not sure business or person who sells goods to consumers deposit money that you put down first instalment with the balance being paid later
Sharing learning	Teacher comments on personalised learners docs and their blogs	Learners blog their learning experience and comment on peers blogs
Next steps	Curriculum Integers	Daily life Daily temperatures Credit and debt Sea level (height above and below)
Reflection	Much enthusiasm was generated as learners compared their selected home with peers and some even ventured to homes in other countries - this will lead to exchange rates and ratio at a later stage

Number	Integers	Year 9
Teacher practice Constructivist Experiential Differentiation	Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they can do critical thinking and show creativity as they learn (4 C’s for today’s learners)
Learning Outcomes	Level 4: Understand addition and subtraction of integers. Know the relative size and place value structure of positive and negative numbers Level 5: Understand operations on integers
Success criteria Learners are successful if they can understand the size and place value of integers and can understand operations on integers SOLO Taxonomy Pre structural Uni structural Multi structural Relational Extended abstract I need help I can Identify I can describe a procedure and do calculations with Integer problems in context I can explain and organise my thinking to solve Integer problems in context I can create and predict solutions and reflect on my answers
Do Now (Introduction)	Google today’s temperature in Auckland.   240C Choose a country or city in the Northern hemisphere and write down their temperature. Use Google maps if you need help finding a city or country. Russia, -20C. Discussion about why other countries are not as warm as Auckland. How much warmer is it in Auckland? Discussion about writing learners’ answers using mathematical statements like  240C - -20C Find at least 1 other Google image to help you understand when we use integers and then explain what an integer is in your own words.
Lesson sequence	Write a mathematical equation for each of the following. Sela has $7 and finds $4 in her bag. How much does she have altogether? Tere has 7 lollies and gives 4 away. How many lollies does she have left? Tui is standing on a strip of blue tape. He takes 4 steps back and 7 steps forward. How many steps is he away from the tape? Maia is standing in a lift at an entrance to a mine. The lift stops 7m below ground level  to drop off supplies and then makes a final stop 4 m further. At what depth did the lift make its final stop?                   7 + 4 = 11               7 - 4 = 3                  -4 + 7 = 3             -7 - 4 = -11 Integers in daily life Explore learning using online resources Make learning visible by creating personalised notes documenting evidence of learners’ understanding of Integers
Learning Experiences	Developing a number sense by exploring number in the context of everyday experiences and the world around them. Using numbers to explore events in their own lives. Developing mental strategies for adding, subtracting, multiplying, and dividing positive and negative numbers, using a calculator, a variety of models, and other approaches Solving problems involving positive and negative numbers
Resources	Google images Google maps Google document Teacher’s Google Number  site
Sharing learning	Teacher comments on personalised learners docs and their blogs	Learners blog their learning experience and comment on peers blogs
Next steps	Curriculum Solving number problems in context	Daily life Understanding and interpreting everyday number contexts
Reflection	The use of images hooked learners into understanding what integers are and the use thereof; particularly the use of integers in daily life

Number	Number in context	Year 9
Teacher practice Constructivist Collaboration	Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so that they can do critical thinking and show creativity as they learn (4 C’s for today’s learners)
Learning Outcomes	Level 3: Describe a procedure and do calculations with Number problems in context Level 4: Explain and organise thinking to solve Number problems in context Level 5: Create and predict solutions and reflect on answers
Success criteria Learners are successful if they can solve number problems in context SOLO Taxonomy Pre structural Uni structural Multi structural Relational Extended abstract I need help I can Identify I can describe a procedure and do calculations with Number problems in context I can explain and organise my thinking to solve Number problems in context I can create and predict solutions and reflect on my answers
Do Now (Introduction)	Review images, notes, explanations, examples and challenges on your Number doc
Lesson sequence	Review learning on the Number topic to date Attempt and solve a contextual task to give learners an indication of their achievement Trip to Wellington 24 students in 9KLe were planning a trip to Wellington in September with the lovely Mr Mansell. The cost of the trip was $80 per student. The group had a sausage sizzle to raise funds. They needed 8 loaves of bread. Elstree Dairy had bread for $2.20 each, but the owner gave them a 15% discount. Students also bought $50 worth of sausages. Onions and tomato sauce were donated by the Geek Cafe. Students sold 110 sausages for $1.50 each and then had a bake sale a few days later. All baked goods were donated and students made a profit of $250. Mrs Dunn offered to donate ⅕ of the amount raised at the bake sale.  How much would each student have to pay? Statement Working Answer (units) Total cost of trip $80 x 24 $1 920 Bread 8 x $2.20 $17.60 Bread discount 15/100 x $17.60 $2.64 Bread cost $17.60 - $2.64 $14.96 rounded $15 Bread + sausage cost $15 + $50 $65 Sausage sizzle $1.50 x 110 $165 Sausage sizzle profit $165 - $65 $100 Donation ⅕ x $250 $50 Bake sale + s sizzle + donation $250 + $100 + $50 $400 Total owing $1920 - $400 $1 520 Payment per student $1 520 / 24 $63.33 rounded $63.30 shortfall $1 520 - ($63.30 x 24) $0.40, so someone will have to pay an extra 40c
Learning Experiences	Apply Number knowledge in real life contexts Collaborate by discussing ideas and possible solutions
Resources	Google document Teacher’s Google Number  site
Literacy strategy	Chunking
Sharing learning	Teacher comments on learners blogs	Learners blog their experience and comments on peers blogs
Reflection	Learners completed a survey (Google Form) Something Old (what learners already knew) Something New (any new learning or strategies gained during the Number strand) Something Borrowed (an aspect of Number that learners taught their peers or vice versa) Something Blue (an aspect of the Number strand that learners still do not fully understand)