MATHEMATICS UNIT PLANNER
Dimension: / Number / Focus: Multiplication DivisionVELS Learning Focus Statement:
In Number, students use patterns and arrays to develop understanding of multiples (including lowest common multiple), factors (including highest common factor), prime and composite numbers. Students devise and use mental and written methods (algorithms) to multiply and divide whole numbers. For division they recognise remainders as common fractions or decimals. They use materials and number lines to develop understanding of multiplication and division of decimals (to two decimal places) and simple common fractions. They routinely make estimations and approximations in calculations and make judgments about their accuracy.Vocabulary Development:
Multiplication, groups of, division, array, row, column, factors, partition division, quotation division,Establishing Prior Knowledge
Multiplication and division Pre-testCommon Assessment Tasks
Assessment FOR Learning / Assessment OF Learning / Assessment AS LearningObservation
Rubrics
Pre-test general knowledge
Student reflection / Completed task
Post-test / Observations
Anecdotal Notes
Other Resources:
Teaching and Learning Sequence
Warm up
/Introduction
(identify &articulate) /Student Learning Activity (including introduction)
/Share / Reflection / Assessment
1 / Pre-TestExtension
2 / Chance and Data
NAPLAN Questions on chance and data – see sheet. / Multiplicative thinking – what is multiplication? Brainstorm words associated.
Discuss Arrays and their properties (rows and columns) – what strategies do people have for remembering which ways rows and columns go?
Discuss that students will be working in different groups. Each group has worksheets with instructions for the activities – LAF 1 students may need guidance to get started. / Scaffolding Maths – You can group different LAF levels together although please keep LAF 1 students in their own group. All grades should include the LAF 1 activity.
Choose at least two other activities for the lesson. Please see sheets provided
LAF 1 – Array Play: May need to introduce by reinforcing what an array is and discussing rows and columns. Students work in pairs. Each person takes a handful of counters. They then arrange counters into as many different arrays as possible, recording number of rows and columns in a table. The person that makes the most different arrays wins that turn. Repeat process 7 times.
LAF 2 – Multiplication toss: Students take it in turns to roll two dice. They then shade in 1cm grid paper to represent the product of the face value on each dice. The student with the most grid paper shaded by the end of activity wins.
LAF 3 – Magicians Costume. Students work in pairs to determine how many different costumes can Same wear? Students record and explain their thinking on A3 sheet.
LAF 4 – Recipe for fruit salad. Students use the recipe provided and adjust it for varying numbers of people, discussing and recording their strategies for the adjustment.
LAF 6 – Square numbers. Students investigate square numbers. Using counters and then grid paper, why 9 and 36 are called square numbers but 24 is not. Students to list all of the square numbers up to 100 and their factors.
LAF 7 – Combining Speeds. Students work in pairs or small groups to solve the Tallangatta to Wodonga problem and then the Melbourne to Sydney problem provided. / 3 minutes rocket writing about what I learnt today.
Possible sentence starters;
A strategy I used today was...
Something I found out......
A feeling I had was...... because...
Support materials
Counters
Dice
Worksheets/scoresheets / Extension
– N/A – activities should be suitable for each student as they will be grouped in ability levels.
3 / Data Warm up:
Using data to order chance events from least likely to most likely.
Using a pack of cards students will investigate/ predict the likelihood of red or black being the next card drawn/how many red or black in a row will occur.
(provided in hard copy) / Dummies guide to worded questions.
Ask students-
Are there any tricks or secrets that you can use when tackling worded problems?
In table groups give students 5 min to discuss and record top 5 tips.
Share whole grade and compile a large class list-Dummies guide for students to refer to during the students learning activity.
Ask students to keep in mind that they will be editing the Dummies Guide after they have completed their sheets- Which tips helped, which need to be edited? / 1=beginning ability
2=consolidated ability
3=established.
Sheet1 B- worded problems multiplication - 2x1 digit numbers.
Sheet 2C- worded problems multiplication - 2x2 digit numbers.
Sheet 3E- worded problems multiplication – 3x2, 3x3, decimal x 2 digit numbers.
See sheets attached below-Each labelled clearly. / Dummies guide to worded problems.
Class/ personal reflection.
Edit the Dummies Guide.
Which tips helped?
Which tips need to be edited?
Discuss as a group and make any needed changes.
Support materials
Cards(warm up)
Large post it for list or butcher’s paper.
Counters
Dice
Worksheets/scoresheets.
Multiplication grid if necessary. / Extension
3 Different sheets to address ability level.
1=beginning ability
2=consolidated ability
3=established.
For extension-if students complete and answer correctly they may attempt the next levels sheet
3=established.
Ask students to produce their own worded questions
4 / Data Warm up:
What might this be a graph of?
Give students an example of a blank pie graph. Students are to discuss and record notes about what the graph might be of.
Class discussion:
Are student’s suggestions reasonable? Why are some more plausible than others? / Revise arrays
Discuss various strategies for solving multiplication problems, emphasising ways that students work out the total without having to draw all the items. / How many chocolates? You have found that the box of chocolates you were given has only a few chocolates left. How many chocolates did it have to start with? Write a story to explain how you worked out the answer.
What if we had a larger box? How many chocolates would there be if there were 12 rows of 8 chocolates? How did you work it out? / Secrets of your Success.
Having noted those children who worked effectively or grasped the concept being introduced well or played the game with great use of strategies/tactics or applied learned skills well – ask 3 or 4 of them to come out to the front (after giving them some advance notice that you will be asking them to do this) front of the class and pass on the “secrets to their success”.
Support materials
You may like to show this clip of students talking about their multiplication strategies.
http://www1.teachertube.com/viewVideo.php?video_id=1603
Students talk about the multiplication strategies they use. / Extension
Partially covered arrays.
Have an array with a small number of dots covered by a piece of paper. Students are to discuss what strategies they would use to determine the number of dots. Students are encouraged to work out how many dots are covered without counting them one by one, or drawing them on the page.
5 / Negative numbers
Clothes Line
Using the cards provided. Hand out 10 numbers and ask the students to place themselves on the clothesline in the correct order. The numbers vary in difficulty so you will be able to choose cards appropriate to individuals.
You must give the parameters. The students then place themselves where they belong. They must justify/explain why they chose the place they did. / Introduction to Division
Language: division, sharing, share between, left over, remainder,
What does division mean?
When do we divide?
What do we divide? Objects, groups, money, food, drinks, distance, time,
What is the purpose for division?
Show some examples of the following strategies. With and without remainders
The Distributive Law
(see explanation below)
Using Number lines
(see explanation below)
Short but ugly
(see explanation below) / Students complete one rich assessment task.
a. Sharing 25 - Yr 4 level
b. Heads & Legs – Yr 5 level
c. Helping Bert Divide –Yr 6 level
These tasks will give you lots of information as to what your kids are doing when they divide.
Choose a task that suits your individual students. Not all students will do the same task. / See/Saw.
In pairs, one person goes first (See) to state something that they learned/recall from today’s lesson/activity. The other person (Saw) then states something they gained from the session. Back to See’s turn. This continues until either See or Saw is unable to recall another fact or aspect of the lesson. Ensure you move among the pairs and encourage use of appropriate terminology. This share activity works very well with about 5 minutes to go before recess time. Person with the last given fact goes out first!
Support materials
*Clothes line number cards
*Pegs
*Worksheet for assessment tasks / Extension
Introduce decimals in the intro for those students who are ready
6 / Four corners:
In each corner of the room attach a clearly seen Club, Spade, Diamond and Heart. Tell students you are going to turn over one from a deck of cards. Chn. go to the corner of the suite they believe will be turned over.
/ Pose the question how many halves in 13, then progressively work towards quarters, 3rds, 5th, and 10ths. Students look for patterns and a way to predict a different number – decimals where appropriate. / See/Saw.
In pairs, one person goes first (See) to state something that they learned/recall from today’s lesson/activity. The other person (Saw) then states something they gained from the session. Back to See’s turn. This continues until either See or Saw is unable to recall another fact or aspect of the lesson. Ensure you move among the pairs and encourage use of appropriate terminology. This share activity works very well with about 5 minutes to go before recess time. Person with the last given fact goes out first!
Support materials
Deck of cards
Counters / Extension
7 / Post -Test
Support materials / Extension
Name: ______Date:______
Worded Problems (multiply by a 2 digit number)
Sheet 1B
Write the number sentence for each of these worded problems and solve. Please show your working out. Eg 4x3=12
a). There are four kids in each of the 14 taxis. How many kids are in all the taxis?
b). 16 Students were playing tennis. They all had six tennis balls each. How many balls do they have in total?
c). How many people do you have in 13 vans if each van has seven people in it?
d). Mrs Brown has eight flower pots in each tray. If she has 23 trays how many flower pots does she have?
e). There are 28 Crows sitting in a tree. How many feet are there altogether?
f). There are 31 butterflies. Each butterfly has 6 black dots and 3 yellow dots. How many black dots are there altogether?
g). There are 9 lions and 6 tigers in a circus show.
How many legs are there in all?
Write your own worded questions and solve. Must include multiplication and at least one number must be larger than 13.
Teacher’s Answer Sheet
Worded Problems (multiply by a 2 digit number)
Sheet 1B
a). There are four kids in each of the 14 taxis. How many kids are in all the taxis?
14x4= 56
b). 16 Students were playing tennis. They all had six tennis balls each. How many balls do they have in total?
16x6= 96
c). How many people do you have in 13 vans if each van has seven people in it?
13x7= 91
d). Mrs Brown has eight flower pots in each tray. If she has 23 trays how many flower pots does she have?
8x20= 160 / 8x3= 24 / 160+24= 184 or 8X23= 184
e). There are 28 Crows sitting in a tree. How many feet are there altogether?
28x2= 56
f). There are 31 butterflies. Each butterfly has 6 black dots and 3 yellow dots. How many black dots are there altogether?
31x6= 186
g). There are 9 lions and 6 tigers in a circus show.
How many legs are there in all?
9+6=14 14x2= 28
Name: ______Date:______
Worded Problems
Sheet 2C
Write the number sentence for each of these worded problems and solve. Please show your working out. Eg 4x3=12
a). There are fourteen kids in each of the 14 cabins at camp. How many kids are in all the cabins at camp?
b). 16 Students were playing tennis. They all had 2 packets of six tennis balls each. How many balls are there in total?
c). How many people do you have in 33 mini buses if each mini bus has 19 people in it?
d). 1-Sarah Smith sells flowers wholesale. Each tray has fourty eight flower pots in them. If she sells 23 trays on Monday, how many flower pots did she sell?
2- If each pot sells for $8, how much did she make from the sale above?
e). Facebook receives 48 new members every second. How many new members are there in 1 minute?
f). There are 89 butterflies. Each butterfly has 26 tiny black dots and 3 large yellow dots on their wings. How many black dots are there altogether?