lesson topic/focus: mental strategies for multiplication

November 27, 2013 LESSON PLAN 1.2: MATHS

Lesson topic/focus: Mental strategies for multiplication: Groups of Grade/levels: 3

AUSVELS Domain: Mathematics Duration: 40mins

AUSVELS Dimension: Number & Place Value

Standard/Learning outcomes:

Students can recall multiplication facts of two, five and ten and can represent and solve problems involving multiplication using efficient mental and written strategies.

Assessment; Success criteria:

Confidently uses arrays to solve multiplication problems.

Assessing prior knowledge:

Quick discussion about topic and reflection on previous lesson:

• Terminology; groups of, lots of • Game; discuss explicit description • Process of repeated addition 3x3= 3+3+3

Lesson resources:

• White board/markers • Work books • Counters • Ten sided dice • A3 paper • strips

Introduction:

Tuning in-

• Students told about learning focus of the day; “We’re going to progress from yesterday’s lesson because we ran out of time and I don’t think that everyone had a in depth learning experience of what multiplication really means especially understanding the idea of having and making groups of”.

• Ask students to stand up and get into:

4 groups of 5 2 groups of 10 7 groups of three


Whole-

• Students discuss with buddies why we completed the activity. • Respond to the group, try and get students to express mathematical terminology

related to multiplication. • Write on the board examples of groups of sentences:

4 groups of 2 4 x 2 2 x4 4 lots of 2 1 1 1 1 1 1 1 1 circle the groups and relate each back to terminology.

• Ask the students to come up with a groups of sentence, multiplication problem in numbers and symbols.

• Model what you want the students to do when in their activity time; “You will be working with these (pre-made problem strips) which tell you how many groups and how many to out into those groups. - In pairs use counters to model what the strip tells you and your partner checks you

have done exactly what it said and you then write the problem in numbers and symbols. Then swap over.

• Model

• After you feel confident with this you can go back to the game we played yesterday. • Discuss the relevance to the game: “Now remember back to yesterdays game, this is

what I wanted you to be doing, I don’t think everyone understood what to do and how to do it, so I’ll show you again”. Model rolling the dice and discussing that this gives you the number of groups to make. Model picking up a random card and this tell you the amount to put in the groups. (Drawing the groups and numbers on the board)

• Why do you think I made up this game? • Prompt to get: groups of, lots of and so on.

Body/Part:

• Strips activity: Students work with pre-made problem strips which tell them how many groups to make and how many to put into each of those groups. - In pairs use counters to model what the strip tells you and your partner checks you

have done exactly what it said and you then write the problem in numbers and symbols. Then swap over.

Skip to solve return:

• Creating groups of from rolling a ten sided die and picking up a playing card, modelling the groups with a concrete material and then writing the problem and the display on a poster.


• Roll a ten sided die (this tells you how many groups to make) • Picking up a playing card (how many to put in each group)

Scaffolding activity: (for students who need that extra time and support)

• Use counters to aid skip counting, and to show the groups of relationship. They also roll a die (6 sided) and flip a card and model creating the groups with counters continuously (with the aid of the teacher). Early finishers/Extension activities:

• Students will be asked to create their own version of the game using the other cards as other numbers etc. They will be asked to write down how to play their game and share this with others. Closure:

• Students attention will be gained and closure. • Reflection: (answers will be recorded on an A3 piece of paper, for referral if needed).

Students will be asked to bring their work back to the floor to share their thoughts with the group.

- What do you think about this strategy? - Good or bad, why? - What did you learn in the activities? - What do you think about multiplication now what is it about?

December 12, 2013 LESSON PLAN 12: MATHS

Lesson topic/focus: Angles: Grade/levels: 3


AUSVELS Dimension: Measurement & Geometry


Students can identify angles as measures of turn and compare angle sizes in everyday situations.


Acknowledges that angles can move, rotate and change as they are turned.


Quick discussion about topic

Lesson resources:

• Work books • String/wool • Tacks • Analogue clock

Introduction:

Tuning in/Whole-

• Give each student two pieces of wool/sting, ask them to create an angle • Now ask them to turn one of the pieces of string left or right in a circular motion (like

a clock) • Discuss with them what is happening; discuss how angles are created as lines rotate

(clock motion). • Model different sizes, ask students to create three different sized angles by moving the

string in different directions (circular motions). • Model this on an analogue clock • Ask the students if they remember the different names for different sized angles. • Model acute, right and obtuse angles. • Discuss quarter turns and how they can be the same angle but rotated to look

different. • Ask students to have a go with their string.

Body/Part:


• Have students walk around the room and search for all the different types of acute, right and obtuse. Students use their string to compare the sizes of different angles. (They record this in their books and label the different types)


• Sit with the student/s on the floor and revisit working with a clock to show the students how angles can be the same but be turned/rotated.

• Ask the student to have a go Early Finishers activity:

• Students who finish early can draw clocks in their books and find the same angles that are shown as different times, eg. three o’clock and quarter past six. Closure:

• Students attention will be gained and closure. • Reflection:

- Students will be asked to bring their work back to the floor to share their thoughts with the group.

- “What did you learn?” - “What did you find out today?”


Lesson topic/focus: Angles: Moving angles Grade/levels: 3






Acknowledges that angles can move, rotate and change as they are turned.



Lesson resources:

• Work books • String/wool • Tacks • Analogue clock

Introduction:

Tuning in/Whole-

• Give each student two pieces of wool/sting, ask them to create an angle • Now ask them to turn one of the pieces of string left or right in a circular motion (like

a clock) • Discuss with them what is happening; discuss how angles are created as lines rotate

(clock motion). • Model different sizes, ask students to create three different sized angles by moving the

string in different directions (circular motions). • Model this on an analogue clock • Ask the students if they remember the different names for different sized angles. • Model acute, right and obtuse angles. • Discuss quarter turns and how they can be the same angle but rotated to look

different. • Ask students to have a go with their string.


Body/Part:

• Have students walk around the room and search for all the different types of acute, right and obtuse. Students use their string to compare the sizes of different angles. (They record this in their books and label the different types)

• Students then use a clocks hand out to create the same angles that are shown as different times, eg. three o’clock and quarter past six.


• Sit with the student/s on the floor and revisit working with a clock to show the students how angles can be the same but be turned/rotated.

• Ask the student to have a go Early Finishers activity:

• Students who finish early Closure:





Lesson topic/focus: Angles: When two lines meet Grade/levels: 3






Acknowledge and model different types of angles



Lesson resources:

• Work books • String • Tacks

Introduction:

Tuning in-

• Students sit quietly on the floor. • Teacher uses two pieces of string to model different types of angels

- As students if they can see how the two lines meet - Explain that when two lines meet that it forms an angle - Rotate the string to create different angles

• Ask the students if they can make the angles with their piece of string on the floor.

Whole-

• Ask students to walk around the room with their books and find different angles, and draw them.

• Students come back to the floor and discuss what they found • Ask students to come up and draw the different angles

- Ask the students if they know what any of them are called? - Discuss the differences between acute, obtuse and right angles and model these /

label examples students give.


Body/Part:

• Students use magazines/newspapers and cut out pictures of angles, paste them in their books and label them according to their type.


• Ask the students to draw all of the different types of angles and label them. Early Finishers activity:

• Students can draw a picture using “paint” or just drawing in their books, using as many angles as they can. When they are finished they swap with a partner and circle all of the angles they can find. Closure:





Lesson topic/focus: Angles: Searching for lines Grade/levels: 3






Confidently finds a variety of lines within many everyday situations.



Lesson resources:

• Work books • Drawing lines activity

Introduction:

Tuning in-

Ask the students to walk around the room and record all of the different lines they can: they may draw them or use words to describe them. (They will be given a few minutes).

Whole-

• Students come back to the group and discuss what they found. • Discuss all the different types of lines (straight, curved, parallel etc). • Ask students to come up and draw examples on the board, and ask students to

describe them (record on board). • Discuss that the world is made of many different types of lines, and lines are very

important for many things; building, furniture, (ask students). • Describe activity

Body/Part:

LABLE THE LINES: • Students write headings for all of the different types of lines

- They then go around the room and draw as many examples of the types of lines they can.


- They then come back and sit with a partner and each draw a picture using all of

the types of lines and they swap their books and label all of the lines (they try and see if their partner can find all of the lines).

Scaffolding activity: (for students who need that extra time and support) • Students work with the teacher and revisit the discussion about the different types of

lines, the teacher may draw examples and ask the student to label them, and ask them why they think the label matches the example (as it describes the line).

• Then ask the student to proceed through the activities with aid from the teacher, until the student feels confident to move on by themselves. Early Finishers activity:

• Students complete activity where they have to follow the instructions to draw specific lines to create pictures (diagonal, straight, curved, horizontal & vertical), they then ask a partner to find all of their lines in their pictures. Closure:





Lesson topic/focus: Mental strategies for division: Arrays Grade/levels: 3




Students can recall multiplication facts of two, three, five and ten and can represent and solve problems involving division using efficient mental and written strategies.


Confidently uses arrays to solve division problems.



Lesson resources:

• Work books: grid paper • Counters • Example arrays

Introduction:

Tuning in-

Ask students to write down a number on a sticky note.

Half of the students will write the number of rows the array will have and the other half will write the number of columns the array will have.

Each student will then pair up and see if they can create the array with counters and solve the problem.

Whole-

• Students will return to the group and share how they solved their problems and will be asked how they think arrays help with solving division/sharing problems.

• Teacher will discuss and refresh students about shared between • Ask students about arrays, and ask them to come up with one on the board

- Refresh columns and rows (depending on the way you look at it down/across)

Body/Part:


• Students use pre made arrays to work out and write down all the things they can find

out from the array: - Shared between both (÷) - Groups of (x)

They must also draw the array and write this in their maths book and work with a partner and check each other’s work.

Scaffolding activity: (for students who need that extra time and support) • Teacher spends time on the floor going through the examples on the board again, and

going through several arrays with the student/s using terminology and focusing on what they need to do. Early Finishers activity:

• Students who finish early can work on the more difficult arrays. Closure:



- What do you think about this strategy? - Good or bad, why? - Where would you use this strategy? (Talking partners)

MISSING SYMBOL:

• Teacher presents a problem and does not show the operation symbol and the students have to decide whether they think the division or multiplication symbol is missing. -If they think the division symbol is missing they stand - If they think the multiplication symbol is missing they kneel Teacher does this three or four times in order to reflect and summarise learning from last two weeks.


Lesson topic/focus: Mental strategies for division: Arrays Grade/levels: 3






Confidently uses arrays to solve division problems.


Quick discussion about topic, in the form of a brainstorm or mind map.

Lesson resources:

• Work books: grid paper • Counters • Dice • Example arrays • Playing cards

Introduction:

Tuning in-

Ask students to write down a number on a sticky note.

Half of the students will write the number of rows the array will have and the other half will write the number of columns the array will have.

Each student will then pair up and see if they can create the array with counters and solve the problem.

Whole-

• Students will return to the group and share how they solved their problems and will be asked how they think arrays help with solving division/sharing problems.

• Teacher will discuss and refresh students and ask about division terminology • Use an example on the board to model how arrays work and how they help solve

division problems: 20 ÷ 5 - Arrays show how many there are altogether 20 - That there are five rows, so there is four in each row


Body/Part:

CUT OUT ARRAYS • Students cut out three arrays and work out the division problems that they make, this

will help them become more familiar with the idea of arrays being related to division sums.

• Students then have to think of how arrays help solve division problems, by rolling dice to create a sharing sum then draw/colour in the array on grid paper (write the sum in the middle of the array).


• Spend more time working with the first activity, where students cut out arrays on grid paper and work out the division sums to match these. The teacher may have prepared arrays for those students to work with so they can familiarise themselves with the process. Early finishers/Extension activities:

• Students create different arrays using two ten sided dice and a playing card, students have to also figure out the multiplication problem and find the answer (record all sums and answers). Closure:




MISSING SYMBOL:

• Teacher presents a problem and does not show the operation symbol and the students have to decide whether they think the division or multiplication symbol is missing. -If they think the division symbol is missing they stand - If they think the multiplication symbol is missing they kneel Teacher does this three or four times in order to reflect and summarise learning from last two weeks.


Lesson topic/focus: Mental strategies for division: Fair/Not fair Grade/levels: 3






Confidently work with an understand fair/not fair (remainders).



Lesson resources:

• Work books • Counters • Playing cards

Introduction:

Tuning in-

• Choose two students and share counters with them (tell the group that the counters are lollies).

• 13 lollies share 6 and 7. -discuss with students and ask if they think this is fair or not and why - ask the students what they would do with the one left over? - ask the students what they think the left over is often called in maths

Whole-

• Students told about learning focus of the day; “Today’s lesson we will be focusing on left over’s”

• Discuss and model another example on the board with the students and ask them what the left over is and what to do with it. - Model what to do with the left over (remaining number/s) r 2

• Discuss activity:

Body/Part:


REMAINDER 1-9

Using playing cards (take out the picture, 10 and joker cards)

• Students pick up three cards and make one two digit number and use the other single digit number to create a sharing problem. - Eg). 53 and 5 students

• Students model the sum with counters and solve, they must separate the remainders to the side and record the problem in their math books

• They also make a table in their books with categories - Remainder 1 - Remainder 2 etc to Remainder 9

Students see how many problems they can make and put into each category.

Scaffolding activity: (for students who need that extra time and support) Students will be encouraged to work with simple problems to gain an understanding of working with remainders. The teacher can work with students to prompt them and keep asking them what to do with the “left over’s” and to model putting them aside otherwise the answer is “not fair”. Early finishers/Extension activities: Students will be encouraged to see if they can make larger remainders by using two 10 sided dice and one playing card. Closure:





Lesson topic/focus: Mental strategies for division: two sentences/groups of Grade/levels: 3






Confidently works with



Lesson resources:

• White board/markers • Work books • Counters • A3 paper • Think boards

Introduction:

Tuning in/Whole-

• Whole class attention will be gained, and the students will be asked to sit quietly on the floor.

• Students told about learning focus of the day; “Today’s lesson we will be focusing on groups of and representing problems as two different questions”

• Eg). If I have 18 apples and I need to share them into equally into 6 bags (6 groups/lots of 6). I could also write this as if I have 18 apples and I have 3 in each bag how many bags do I need? - Discuss similarities and differences between questions.

(1# how many groups asks how many in each group. 2# how many their is in each group, asking how many groups there are.

Body/Part:

THINK BOARDS: Students use think boards to model two sentences of the same problem, to show and create an understanding of using two bits of information enabling them to think of this as another effective strategy.


Use dairies to find tricky sharing problems to solve in two ways. Scaffolding activity: (for students who need that extra time and support) Students will be encouraged to work with simple sharing problems and model them whilst the teacher aids them and prompts them in the process. Early finishers/Extension activities: After students have had a go at completing problems that they find they need to work on, they may begin to work with harder problems. Eg). They may roll a ten sided di twice to come up with different problems or two ten sided dice. Closure:




November 29, 2013 LESSON PLAN 4: MATHS

Lesson topic/focus: Mental strategies for multiplication: Arrays Grade/levels: 3




Students can recall multiplication facts of two, three, five and ten and can represent and solve problems involving multiplication using efficient mental and written strategies.


Confidently uses arrays to solve multiplication problems.



Lesson resources:

• White board/markers • Work books • Counters • Ten sided dice • Sample array • A3 paper • Example of the strip book

Introduction:

Tuning in/Whole-


• Students told about learning focus of the day; “Today’s lesson we will be focusing on arrays”

• What do you know about the word “array”? (Record answers on the board in the form of a mind map).

• Draw an array on the board eg). 4 x 5 • Discuss how the dots are associated with the answer; the row and the column

Eg) the row has .....dots in it and the column has.....dots in it therefore it is showing us the problem and the answer.


Body/Part:

MAKING ARRAYS:

• Each student will be given some A3 paper to create their own array; they will need to think of a problem and to write it down. They will then create their array and use coloured pencils to colour it in. (An example will be available to look at).

• Students also use their array to write a sentence about it; Eg) 5 rows of 3 = 15 (5 x 3 = 15) 3 columns of 5 = 15 (3 x 5 =15) Scaffolding activity: (for students who need that extra time and support)

• Students will be given an A3 sample array which they throw a ten sided die twice and create a problem. They then have to colour in the dots of the problem and the teacher shows them how to do so (if necessary). Early finishers/Extension activities:

• Students can create their own strip books where they think of a multiplication sequence they are having trouble with and create a modelled book of the problems. This is created by folding a piece of paper into the required amount of sections needed for the problem.

This will help the students as they will be encouraged to refer back to this if they require it during other lessons. Closure:

• Students attention will be gained and closure. • Reflection: (answers will be recorded on an A3 piece of paper, for referral if needed).


- What do you think about this strategy? - Good or bad, why? - Where would you use this strategy? (Talking partners) - Will you keep your books or arrays to refer back to help you with another

problem?


Lesson topic/focus: Mental strategies for multiplication: Place Value in multiplication Grade/levels: 3




Students can recall multiplication facts of two, three, five and ten and can represent and solve problems involving multiplication using efficient mental and written strategies.


Confidently use the place value strategy when working with multiplication problems.


Tuning in activity: groups of modelling

Lesson resources: • White board/markers • Work books • Counters • Unifix/MAB • Playing cards • Ten sided dice

Introduction:

Tuning in-

• In pairs students will create groups of ones and groups of tens for the multiplication problems, using MAB/unifix or counters.

• The teacher will present a problem on the board: 5 x 1 = the students need to put the materials into groups of the problem.

• The teacher will ask how many counters were in the problem? Can you tell me anything significant about that?

• Next the teacher will pose another problem: 5 x 10 = • Again the teacher will ask the students if they can see anything significant about the

problem and the way they are working. • Repeat with other problems if necessary.

Whole-



• Students told about learning focus of the day; “Today’s lesson we will be focusing on

the place value strategy” • Discuss tuning in activity; using an example 7 x 1 =

If I draw this on the board like this 0000000 meaning one group of seven the answer is...... 7 x 10 = 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000 0000000

• Discuss groups of and refer to division if all students understand.

Body/Part:

GROUPS WITH COUNTERS: Students (in pairs) will have a ten sided die and they will take it in turns to roll the die twice and receive a problem, they can solve using counters to create the groups and draw them in their book. Students can also provide the multiplication problem in their book next to the drawing. Scaffolding activity: (for students who need that extra time and support) Teacher will go through the activity with the students in stages so that they can begin to understand the process of what to do and what is important about the activity. Early finishers/Extension activities: Students can work with bigger problems such as 5 x 20, 3 x 30, 4 x 40 and ask them to use the groups with counters activity or another previously learned strategy and compare the two. Closure:


Students will be asked to bring their work to the floor and share their discoveries with the group. - What do you think about this strategy? - Good or bad, why? - Where would you use this strategy? (Talking partners)


Lesson topic/focus: Mental strategies for multiplication: Halving & doubling Grade/levels: 3




Students can recall multiplication facts of five and ten and can represent and solve problems involving multiplication using efficient mental and written strategies.


Confidently solve multiplication problems using the doubling and halving strategy.


Discussion/talking partners of the prompt:

- What is a half? - What is doubling?

Lesson resources:

• White board/markers • 5x & 10x tables laminated • 10 sided dice • Work books • Multiplication grid

Introduction:

Tuning in-

Teacher calls out numbers and students have to physically get into those groups.

The teacher then says halve or double and students need to halve or double the size of their group.

Whole-


• Students told about learning focus of the day; “Today’s lesson we will be focusing on halving and doubling as a strategy when working with multiplication”.

• Discussion/talking partners of the prompt what is a half, what is doubling? • Responses will be recorded on the whiteboard.


• Teacher will use 5 and 10 times tables with blank answers to ask the students to

produce the answers by using different strategies. • As each child explains their strategy they will be recorded on the whiteboard. • Talk about similarities (doubles and halves) - “We can multiply an unknown by ten and halve it to gain the correct answer” and vice

versa. • Model this on the board

eg) 4 x 5 – 4 x 10= 40 halve it = 20 4 x 5 = 20 4 x 10 = 40 • Allow students to complete more examples together on the whiteboard as needed.

Body/Part:

CONTINUOUS ROLL:

Students create multiplication problems and solve them through rolling a ten sided dice and multiplying the number by five and/or ten and record their answer, using the strategies doubling and halving.

They write down their equations as they proceed.

Students work in pairs and see who gets the highest number after 10 rolls.


Using the multiplication grid and counters students fill in the banks using the doubling and halving strategy.

Early finishers/Extension activities:

Students will come up with larger multiplication problems and use unifix blocks to model these problems.

They will also use the small whiteboards to show their working as they double the problem and then halve it to come to the correct answer,

eg). 23 x 10 = 230 23 x 5 = 115 Doubling Halving

Closure:

• Students attention will be gained and closure. • Reflection: Students will be asked to bring their work with them to the floor to discuss

what they found throughout the activities.


- What do you think about this strategy? - Good or bad, why? - Where would you use this strategy? (Talking partners) - How did doubling and halving help you solve the problems? Why/how?


Lesson topic/focus: Mental strategies for multiplication Grade/levels: 3




Students can recall multiplication facts of two, three, five and ten and can represent and solve problems involving multiplication using efficient mental and written strategies


Confidently highlight number facts for specific sequences (2, 3, 5, and 10), create problems and solve them by skip counting.


Discussion/talking partners of the prompt what is multiplication? (What does this mean x?)

Lesson resources:

• White board/markers • Counters • 100 charts • Highlighters • Playing cards • Small whiteboards • 10 sided dice

Introduction:

Tuning in-


• Students told about learning focus of the day; “Today’s lesson we will be focusing on • Discussion/talking partners of the prompt what is multiplication? (What does this

mean x?) • Responses will be recorded on the whiteboard. • “With your talking partner see if you can come up with one problem shown in

counters”.


Whole-

• Skip counting with number chart aid: 2’s, 3’s, 5’s and 10’s • Asking students if they can see any patterns (model highlighting using different

markers). • “Choose a number” and we will skip count together to reach the answer. • Do you think this will be a good strategy to use when you are working with

multiplication tasks? Body/Part:

• Explain rotation tasks: 100 HIGHLIGHT Students use 100 charts to highlight multiplication facts for each sequence (2, 3, 5 & 10’s). Students also write these patterns down and model with counters to make sure that they fully understand the patterns. SKIP TO SOLVE: Students use a ten sided dice and playing cards to create multiplication problems then solving them by skip counting. Students will be encouraged to use counters and/or draw, in order to record their progress. Scaffolding activity: (for students who need that extra time and support)

• Use counters to aid skip counting. They can also write down their sequence such as + + or 2+2+2=6 2 4 6 Early finishers/Extension activities:

• Students will use small whiteboards whilst working in pairs to create different problems. One: Picks a number. Two: Skip counts till the other says stop (to say they’ve reached the answer). This student snow has to create a multiplication problem that would suit the given answer. Closure:

• Students attention will be gained and closure. • Reflection: Students will be asked to bring their work with them to the floor to

discuss. - What do you think about this strategy? - Good or bad, why? - Where would you use this strategy? (Talking partners) - Did this help you in the activities? Why/how?

lesson topic/focus: mental strategies for multiplication

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