Download Extending Mathematical Understanding

EXTENDING
MATHEMATICAL
UNDERSTANDING
INTERVENTION PROGRAM
SPECIALIST TEACHER MANUAL
Ann Gervasoni
Australian Catholic University
Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services
EXTENDING
MATHEMATICAL
UNDERSTANDING
SPECIALIST TEACHER MANUAL
Ann Gervasoni
Publisher: Ballarat Heritage Services
PO Box 2209, Ballarat, VIC 3354
www.ballaratheritage.com.au
Revised Edition
© 2010 Ann Gervasoni
Copyright is vested in the author. The moral right is claimed.
This work is copyright. Apart from any fair dealing
permitted according to the provisions of the Copyright Act
1968, no part may be reproduced, photocopied, stored in any
type of retrieval system or transmitted by any means or
processes whatsoever without the prior written consent of the
author or publisher.
While reasonable efforts have been made to ensure the
contents of the publication are factually correct, Ballarat
Heritage Services does not accept responsibility for the
accuracy of completeness of the content, and shall not be
liable for an loss or damage that may be occasioned directly
or indirectly through the use of, or reliance on, the contents
of this publication.
ISBN 978-1-876478-56-X
Cover Design: Ann Gervasoni
Ann Gervasoni with Jessica during an EMU Assessment Interview, January 2003
Photo courtesy of Rosemary Carroll
Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services
3
Extending Mathematical Understanding Assessment Record Sheet
Name:_____________________ Grade:___ School: ______________ Suburb: ___________
Interviewer:_______________________ Date: ______________ Total Hours EMU________
COUNTING FRAMEWORK
1. Handful of teddies (Counting Collections)
Estimate ____ Actual ____ Correct count 
Error sequence (if any) __________________________
Arranges items / touches items randomly (misses items/double counts)
1a. How many now? _____ (one less/recounts ______)
2. Dot cards (1-10).
1  count/subitise/other
2  count/subitise/other
3  count/subitise/other
4  count/subitise/other
5  count/subitise/other
6
7
8
9
10





count/subitise/other
count/subitise/other
count/subitise/other
count/subitise/other
count/subitise/other
3. Rote Counting
1120  (any error sequences)________________________________
4. Conservation Task (6 items)
a. Answer ____  conservation/recounts
b. [Answer ____ ]
5. One to one correspondence (4 items)
a. Answer ____  1/1 correspondence/recounts
b. [Answer ____ ]
6. Handful of Beans (Counting larger collections)
Estimate ____ Actual ____
Correct count 
Error sequence (if any) __________________________
Arranges items / touches items randomly (misses items/double counts)
6a. How many now? _____ (one less/recounts ______________)
7. The Number After
a. After 7 ____  counts on / counts from one
b. After 13 ____ counts on / counts from one
c. After 45 ____ counts on / counts from one
8.
Counting Forward
a. 4355  (error sequence) ______________________________
b. 7893  (error sequence) ______________________________
c. 95122  (error sequence) _______________________________
9. The Number Before
a. Before 7 ____  counts back / counts from one
b. Before 12____ counts back / counts from one
c. Before 46____ counts back / counts from one
40
Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services
10. Counting Backwards
a. 100
 (error sequence) ______________________________
b. 2210
 (error sequence) ______________________________
c. 5448
 (error sequence) ______________________________
d. 9488
 (error sequence) ______________________________
e. 114108
 (error sequence) ______________________________
f. 124118
 (error sequence)
_____________________________
11. Counting by Tens
0120  (error sequence)________________________________
12. Counting by Fives
0110  (error sequence)________________________________
13. Counting by Twos
040  (error sequence)_ ______________________________
PLACE VALUE FRAMEWORK
14. Reading Numeral Cards (0-10)
0 _ 1 _ 2 _ 3 __ 4 __ 5 __ 6 __ 7 __ 8 __ 9 __ 10. __
15. Matching Quantities and Numeral Cards (0-10)
0 _ 1 _ 2 _ 3 __ 4 __ 5 __ 6 __ 7 __ 8 __ 9 __ 10. __
15a. Quantity for ‘8’
8 teddies  other number ____ continues past 8 / recounts/ other________
16. Writing Numerals (0-10)
a. 2 ___ 5 ___ 1 ___ 3 ___ 4 ___
b. 7 ___ 9 ___ 8 ___ 6 ___ 0 ___ 10 ___
17. Ordering Numerals (0-10)
1-5  sequence _______________
6-9  sequence ________________
Orders the 0 card correctly 
Orders the 10 card correctly 
18. Reading Numerals (ranges: 11-19)
11 __ 12 __ 13 __ 14 __ 15 __ 16 __ 17 __ 18 __ 19 __
18a. Reading Numerals (ranges: 20-29; 30-49; 50-99; 100-300)
20-29  errors_______________
30-49  errors_________________
50-99  errors_______________
100-300  errors_______________
19. Matching cards and pop sticks (2 digit)
Numeral ___  [collects tens & ones / counts decades & ones (10,20,30…) counts by ones / other………
One bundle less ___  [strategy .................................]
Numeral ___  [collects tens & ones / counts decades & ones (10,20,30…) counts by ones / …………
One bundle less ___  [strategy .................................]
Numeral ___  [collects tens & ones / counts decades & ones (10,20,30…) counts by ones / …………
One bundle less ___  [strategy .................................................................]
20. Bundles Answer_____ 
 8 (bundles) integrated
 10 20 30 …80 (sequence tens)
 1, 2, 3…8 tens, that’s 10, 20, 30 …80 (separate tens)
 counts by ones
 other ___________________ Satisfactory explanation 
Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services
41
The EMU Interview
20a.
70 Sticks
Answer_____ 
a. 7 (bundles) integrated
b. 10 20 30 …70 (sequence tens)
c. 1, 2, 3…7 tens, that’s 10, 20, 30 …70 (separate tens)
d. counts by ones
e. other ___________________ Satisfactory explanation
21. Show me 14

Answer______  collects ten & 4 ones / counts decade & ones (10,11,..) / counts by one/ other
_______
22. Writing Numerals (range: 10-19; 20-29; 30-49; 50-99; 100-300).
12 __ 11 __ 16 __ 19 __ 18 __ 14 __ 13 __ 15 __ 17 __
22a. Writing Numerals (range: 10-19; 20-29; 30-49; 50-99; 100-300).
20-29  errors_______________
30-49  errors_________________
50-99  errors_______________
100-300  errors_______________
23. Ordering Numerals (Range: 10-29; 20-29; 30-49; 50-99; 100-300).
a) Orders cards from 10-19.  Sequence ___________________________
b) Orders cards from 20-29.  Sequence ___________________________
c)
Orders cards from 30-49.  Sequence ___________________________
d) Orders cards from 50-99  Sequence ___________________________
e)
Orders cards from 100-300  Sequence__________________________
24. Hundreds Tasks
Correct 621  _________________ error
Strategy
 6 hundreds, 2 tens and 1 ones, that’s 621 (integrated)
 100, 200, 300, …600, 610, 620, 621 (sequence hundreds, tens)
 1, 2, 3 …6 hundreds, 1, 2 tens and 1, that’s 100, 200, 300, …621 (separate hundreds, tens)
 counts by ones
 other ___________________
 Satisfactory explanation 
24a. How many now?
Correct 921  _________________ error
Strategy
 9 hundreds, 2 tens and 1 ones, that’s 921 (integrated)
 100, 200, 300, …900,910, 920, 921 (sequence hundreds, tens)
 1, 2, 3 …9 hundreds, 1, 2 tens and 1, that’s 100, 200, 300, …921 (separate hundreds, tens)
 counts by ones
 other ___________________
 Satisfactory explanation 
24b. Some More
10 more than 392 ________
24c.. Some less
10 less than 308 ________
402/ counts-on/other …………………………………
298 / counts-back all / other ………………………………………..
ADDITION & SUBTRACTION STRATEGIES FRAMEWORK
25. How Many Teddies? (Total <10)
a. Answer ____ [count on / number fact / count all by re-presenting/ other…………………].
b. Answer ____ [count all by touching /count all by re-presenting / other…………………….]
26. How many teddies now? (Total >10)
a. Answer ____ [count on from 8 / count on from 4 / number fact / count-all by re-presenting/ other…...
b. Answer ____ [count all by touching /count all by re-presenting / other……….]
42
27. How many teddies left? (Minuend > 10)
a. Answer ____ [counts back all ( 9, 8, 7 or 8, 7)./ counts all from 1-7 (8, 9) / number fact / models by
re-presenting / other………].
b. Answer ____ [counts all (remainder) by touching /counts all (remainder) by re-presenting / other……
28. How many teddies left now? (Minuend < 10)
a. Answer ____ [counts back all ( 12-4)./ counts up from (8-12) / counts down to (12-8) / number fact /
models by re-presenting / other………].
b. Answer ____ [counts all (remainder) by touching /counts all (remainder) by re-presenting / other……
29. Answer These (circle strategy used)
a. 6+6 Ans ____ doubles or known fact / count on 6 7 8 9 10 11 12 / other……...……….
b. 3+7 Ans ____ tens fact / count on 7 8 9 10 / count on 3 4…10/ other…………………..
c. 2+15 Ans____  commutativity & count on 15, 16, 17/ known fact/other……….……….
d. 24+10 Ans ____ add 10 (24, 34)/ build to next ten (30 then 6)/count on/other……….…
e. 10-8 Ans ____ known fact/fact family(8+2=10) /count back/ down to or up from /other...
f. 25-10 Ans ____ take 10 (25 15)/ back to last ten (20 then 5)/count back/other……….…
MULTIPLICATION & DIVISION STRATEGIES FRAMEWORK
30. Plates & Spoons (Multiples of 2)
Answer ____ [counts all / skip counts / known fact / other…………………………..…….
31. Multiples of five
Answer ____ [counts all / skip counts / known fact / other…………………………..……
32. Pens Task (circle strategy used)
Answer ____ counts all / skip counts / known fact / other…………………………..…….
32a. Answer ____ counts all / skip counts / known fact / other…………………………..…….
33. Dots Array (circle strategy used)
Answer ____
a. Answer_______
• Skip count
• Skip count
• Known fact _______
• Known fact _______
• Count all by 1s • Count all by 1s
• Other ………. …
• Other …………………
34. Bottles in the Box (circle strategy used)
Answer ______
• Share by groups
• Known fact
• Share by 1s
• Other ……….
35. Multiplication Problems
a. 4 x 10 ______ Skip count/ known fact/count all/ other __________________
b. 2 x 6_______
Skip count/ known fact/count all/ other __________________
c. 10 x 6 ______ Skip count/ known fact/count all/ other __________________
d. 4 x 50 ______  Skip count/ known fact/count all/ other __________________
e. 3 x 40 _____
Skip count/ known fact/count all/ other __________________
f. 5 x 6 _____
Skip count/ known fact/count all/ other __________________
36. Sharing Spoons
Answer ____ [shares by ones/ shares in groups / skip counts /known fact / other………….…
37. Sharing More Spoons
Answer ____ [shares by ones/ shares in groups / skip counts /known fact / other….………….
Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services
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Chapter 6
EMU Templates
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Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services
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1
Gervasoni, A. (2010) EMU Program Sample
Gervasoni, A. (2010) EMU Program Template 1
9 7 5 3 1
8 6 4 2 0
Chapter 6
64
104
123
167
212
254
65
1
115
141
207
231
299
Gervasoni, A. (2010) EMU Program Sample
Chapter 6
308 392
4×10
621
Gervasoni, A. (2010) EMU Program Template 1
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Gervasoni, A. (2010) EMU Program Sample 1
Chapter 6
Gervasoni, A. (2010) EMU Program Template 1
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Mathematics Individual Learning Plan Sample
Name: Annie
Year Level: 2
Date of Birth: 14 March 1994
Classroom Teacher:
Ms Gallo
Intervention Teacher: Mrs Gaio
For the period: 1 March to 31 March
Mathematics Focus:
This Individual Learning Plan will focus on experiences that will assist the child reach the following growth points:
Counting:
1. Rote counts to
at least 20
Place Value:
Addition & Subtraction
Strategies:
Multiplication &
Division Strategies:
2. Counts a collection 3. Counts forwards &
4. Skip count by
5. Skip count by 2s,
of about 20 items
backwards by ones, from
2s, 5s & 10s
5s & 10s from X
any starting point
1. Reading, writing,
2. Reading, writing,
3. Reading, writing,
4. Reading, writing,
interpreting and ordering
interpreting and ordering
interpreting and ordering
interpreting and
single digit numbers.
ordering 2 digit numbers.
3 digit numbers
4 digit numbers
1. Count all
2. Count on
3. Count back/Counts down 4. Basic Strategies
to/ counts up from
1. Count all (multiple groups)
2. Modelling multiplication & division 3. Abstracting multiplication and
when all items are perceived
division
Classroom Activities:
Counting
Place Value
Addition & Subtraction
Multiplication & Division
 Counting items in collections
(20-30 items) co-ordinating
words with items being counted.
 Focus attention on the need to
strategically separate counted
items from those still to be
counted. Ask for an explanation
about why this is necessary.
 Locating numbers on a vertical
number lines.
 Using number lines and
counting charts that extend
beyond 110 to support
backwards counting from
various starting points.
 Backwards calculator counting
with the challenge of predicting
the next 3 numbers (range 150120). e.g., p. 50.
 Partitioning collections into
parts (with stated targets) and
counting how many left over.
 Skip counting activities starting
from random numbers. e.g.,
Five Before Bingo (p. 50).
 Activities involving naming
numbers 3/5/10 before/ after a
given number.
 Using materials in tens (e.g.,
pop sticks in bundles of tens
and loose ones) to make
collections matching
numerals (range 30-99).
 Ordering numerals (range
30-99) and explaining why a
number is more of less,
smaller or larger than
another. Use materials to
demonstrate smaller and
larger group sizes.
 Missing subtrahend tasks (p.
49) for numbers 10-15. Help
Annie become aware of
Count-back strategies.
 Difference of 3 (p. 57). Ask
Annie to demonstrate how
to use count back or counton in this game.
 Two Below Bingo (p. 48).
This focuses Annie’s
attention on counting-back
strategies. Adapt for Three
Below or Four Below.
 Doubles Bingo (p. 58).
Annie is beginning to use
doubles strategies. This
game provides a context to
practise this strategy.
 Open tasks for addition and
subtraction. e.g., Animals in
the Paddock (p. 58).
 What comes in Groups? (p.
60). Encourage Annie to think
about what comes in groups,
and to solve problems using
these groups.
 Sharing Pencils, e.g., p. 61
(adapt this context to create
other similar tasks). This
challenges Annie to share in
groups and focus on group
structures when she is sharing
items. Ask her to predict first
and then use materials to test
these predictions.
 How Many Chocolates (p.
61). Predict then check with
models.
 Array Games (p. 61). This
gives Annie the chance to
make different arrays and
work out the totals.
Encourage her to predict the
total first and then check.
 One more or one less (range
30-99. Choose a numeral and
ask if you had this many
things and you got one/two
more (or lost one/two) how
many would you now have?
 Play in the Middle (p. 51).
Match cards to number line
(e.g., on a tape measure).
 Play Number Target (p. 52)
to highlight place value ideas
for two and three digit
numbers.
 Five Minute Collections (p.
51).
Home Activities: An EMU Maths Bag will be sent home each night. This bag contains a tape measure for counting and ordering, a
calculator for counting backwards and skip counting, pop-sticks in bundles of tens, counters, game boards, e.g., Snakes and
Ladders, playing cards, and die. Tasks will be added to the bag when appropriate. Practising counting and playing these games will
help Annie’s mathematical development. Talk to her about her thinking to help her to notice the mathematics. Play games like
Snap and Fish, but at the end ask Ann to find the total of the “pairs.” Eventually she will automatically remember the totals, but
this will take time.
Comments:
1. Goal Setting: Give Annie the chance to set individual goals for the week. E.g., counting backwards from 60.
2. Reflection: Give Annie the opportunity to notice and explain the mathematics she explored by targeted questioning during
activities and using a reflection time at the en of an activity.
69
1
Gervasoni, A. (2010) EMU Program Sample
Chapter 6
Mathematics Individual Learning Plan
Name: ________________________________
Year Level: _______
Classroom Teacher:
Intervention Teacher: _________________________
___________________
Date of Birth: __________
For the period ________________________ to _______________________
Mathematics Focus:
This Individual Learning Plan will focus on experiences that will assist the child reach the following growth points:
Counting:
1. Rote counts to
at least 20
2. Counts a collection 3. Counts forwards &
4. Skip count by
5. Skip count by 2s,
of about 20 items
backwards by ones, from
2s, 5s & 10s
5s & 10s from X
any starting point
Place Value:
1. Reading, writing,
2. Reading, writing,
3. Reading, writing,
4. Reading, writing,
interpreting and ordering
interpreting and ordering
interpreting and ordering
interpreting and ordering
single digit numbers.
2 digit numbers.
3 digit numbers
4 digit numbers
Addition & Subtraction 1. Count all
2. Count on
3. Count back/Counts down 4. Basic Strategies
Strategies:
to/ counts up from
Multiplication &
1. Count all (multiple groups)
2. Modelling multiplication & division 3. Abstracting multiplication and
Division Strategies:
when all items are perceived
division
Other:
Classroom Activities:
Counting
Place Value
Home Activities:
Comments:
Gervasoni, A. (2010) EMU Program Template 1
70
Addition & Subtraction
Multiplication & Division
Extending Mathematical Learning Progress Summary
Name: ________________________________
Year Level: _____
Date of Birth ________
ENRP Profile: A___ B___ C___ D___ E___ F___ G___ H___ I___ (March ______)
ENRP Profile: A___ B___ C___ D___ E___ F___ G___ H___ I___ (Nov
______)
ENRP Profile: A___ B___ C___ D___ E___ F___ G___ H___ I___ (March ______)
ENRP Profile: A___ B___ C___ D___ E___ F___ G___ H___ I___ (Nov
______)
ENRP Profile: A___ B___ C___ D___ E___ F___ G___ H___ I___ (March ______)
ENRP Profile: A___ B___ C___ D___ E___ F___ G___ H___ I___ (Nov
______)
NOTES:
Date:
Affective Characteristics( e.g. interest, enjoyment, persistence, attitude, motivation)
Program Evaluation:
71
Template 2
Gervasoni, A. (2010) EMU Program
EMU Program Templates
PROGRESS MEETING SUMMARIES
Date
Participants
Gervasoni, A. (2010) EMU Program Template 3
Notes & Recommendations
Action
Taken
72
Extending Mathematical Understanding Assessment Profile Sheet
Counting Knowledge
Number range
0
1
2
3
4
05
010
015
05
010
015
050
090
0120
210
220
240
5
6
7
8
9
020
030
035
020
025
030
100
200
300
520
550
5100
1/1 corresp.
500
900
1200
1050
1090
10120
10
Growth Point
Conservation
Pre-1. Knows some number 1. Rote counts to at least 20 2. Counting Collections(of
names
about 20 items)
3. Counts forwards &
backwards by ones,
from any starting point
4. Skip count by 2s, 5s & 10s
Number Concepts and Place Value Knowledge
Reading
1
2
3
4
5
6
7
8
9
10
015
019
2029
2049
5099
100999
Writing
1
2
3
4
5
6
7
8
9
10
015
019
2029
2049
5099
100999
Ordering
02
04
06
08
010
015
019
2029
2049
5099
100999
Partitioning and
Interpreting
02
04
06
08
010
015
019
2029
2049
5099
100999
Growth Points
1. Reading, writing, interpreting and ordering one digit numbers.
2. Reading, writing, interpreting and ordering numbers to 100
3. 3 digits
Addition & Subtraction Strategies
Addition contexts
Counts all when
items are
perceived
Counts all by re-presenting items
when not directly perceived
(e.g., models with fingers)
Counts on from one
addend
Counts on from
largest addend
Counts the remainder by representing items when not
directly perceived(eg models
with fingers)
Counts the remainder by
re-presenting items when
not directly perceived(eg
models with fingers)
Counts back all
Subtraction contexts
Counts the
remainder when
items are
perceived
Counts down to/
counts up to
010
019
029
2. Count on/
Number range
Growth Points
1. Count all
Doubles, commutativity,
adding 10, subtracting
10, tens facts, other
known facts
Near Doubles,
commutativity,
adding 9,
subtracting 9, 100
facts, other known
facts
Beyond 29
0120
Beyond 120
3. Count back /
down to/ up from
4. Basic Strategies
5. Derived
Strategies
Multiplication & Division Strategies
Multiplication
contexts
Counts all items by ones
when items are perceived
Uses skip counting when all
groups are modelled
Uses known number facts
when all groups are modelled
Determines total by
skip counting
Uses known number
facts to determine total
Division contexts
Shares by ones when items
are perceived
Shares in groups using skip
counting when modelling
Uses known number facts to
determine total
Determines total by
skip counting
Uses known number
facts to determine total
Partitions
2s
Growth Points
3s
4s
5s
1. Count all (multiple
groups)
Gervasoni, A. (2010) EMU Program Template 6.1
10s
2s
3s
4s
5s
10s
2s
3s
4s
5s
2. Modelling multiplication & division when all items
are perceived
73
10s
2s
3s
4s
5s
10s
3. Abstracting multiplication & division when all
items are not perceived
EMU Program Templates
Extending Mathematical Understanding Assessment Profile Sheet B
(Szydzik and Gervasoni, 2006)
Counting Framework
Number range
050
100
500
Growth Point
3. Count forwards &
backwards by ones, from
any starting point
090
200
900
0120 210 220
300 520 550
1200 1050 1090
240
5100
10120
xy
10s
4. Skip count by 2s, 5s & 10s
2s
5s
2s
6s
9s
xy
4s
8s
5. Skip count by 2s, 5s &
10s from any number.
3s
7s
xy
6.Count by any single digit
number from x. Apply counting
skills in practical tasks.
7. Counts by fractions &
decimal fractions from a
non-zero starting point.
Place Value Framework
Reading
015
019
2029
2049
5099
100150
100199
200299
200499
500999
10003000
Writing
015
019
2029
2049
5099
100150
100199
200299
200499
500999
10003000
Interpreting
015
019
2029
2049
5099
100150
100199
200299
200499
500999
10003000
Growth Points
2. Reading, writing, interpreting and ordering numbers to 100
3. Reading, writing, interpreting and ordering 3 digit numbers to 1000 (and
beyond)
Addition & Subtraction Strategies Framework
Addition contexts
Counts on from largest addend
Doubles, commutativity, adding 10,, tens facts,
other known facts
Near doubles, adding 9, build to next 10, fact
families and intuitive strategies.
Counts down to/ counts up to
Doubles, commutativity, subtracting 10, tens
facts, other known facts
Near doubles, adding 9, build to next 10, fact
families and intuitive strategies.
Number range
Beyond 29
0120
0 5 digits, 2 decimal places.
Growth Points
3. Count back / down to/ up from
4. Basic Strategies
5.Derived strategies
Subtraction contexts
Counts back all
Multiplication & Division Strategies Framework
Multiplication
contexts
Determines total by skip counting when all
groups are modelled
Uses known number facts when all groups
are modelled
Uses fact families, builds up from known facts
Division contexts
Shares in groups using skip counting when
modelling
Shares in groups using known number facts
when modelling
Uses fact families, builds up from known facts.
Number range
2s
Growth Points
EMU Assessment Template 6.2
3s
4s
5s
6s
7s
8
9s
2. Modelling multiplication & division when all items are perceived
74
10s
2
3
4
5
6
7
8
9
3. Abstracting multiplication and division
10
Extending Mathematical Understanding Weekly Planning
Counting Knowledge
Number range
0
1
2
3
4
0 5
0 10
0 15
5
6
7
8
9
0 20
0 30
0 35
10
Growth Point
0 5
0 10
0 15
0 50
0 90
0 20
0 25
0 30
Conservation 1/1 corresp.
10 0
20 0
30 0
5 20
5 50
5 100
50 0
90 0
120 0
10 50
10 90
10 120
Pre-1. Knows some number 1. Rote counts to at least 20 2. Counting Collections(of
names
about 20 items)
0 120
3. Counts forwards &
backwards by ones,
from any starting point
2 10
2 20
2 40
4. Skip count by 2s, 5s & 10s
Number Concepts and Place Value Knowledge
Reading
1
2
3
4
5
6
7
8
9
10
0 15
0 19
20 29
20 49
50 99
100 999
Writing
1
2
3
4
5
6
7
8
9
10
0 15
0 19
20 29
20 49
50 99
100 999
Ordering
0 2
0 4
0 6
0 8
0 10
0 15
0 19
20 29
20 49
50 99
100 999
Partitioning and
Interpreting
0 2
0 4
0 6
0 8
0 10
0 15
0 19
20 29
20 49
50 99
100 999
Growth Points
1. Reading, writing, interpreting and ordering one digit numbers.
2. Reading, writing, interpreting and ordering numbers to 100
3. 3 digits
Addition & Subtraction Strategies
Addition contexts
Counts all when
items are
perceived
Counts all by re-presenting items
when not directly perceived
(e.g., models with fingers)
Counts on from one
addend
Counts on from
largest addend
Counts the remainder by representing items when not
directly perceived(eg models
with fingers)
Counts the remainder by
re-presenting items when
not directly perceived(eg
models with fingers)
Counts back all
Subtraction contexts
Counts the
remainder when
items are
perceived
Counts down to/
counts up to
0 10
0 19
0 29
2. Count on/
Number range
Growth Points
1. Count all
Doubles, commutativity,
adding 10, subtracting
10, tens facts, other
known facts
Near Doubles,
commutativity,
adding 9,
subtracting 9, 100
facts, other known
facts
Beyond 29
0 120
Beyond 120
3. Count back /
down to/ up from
4. Basic Strategies
5. Derived
Strategies
Multiplication & Division Strategies
Multiplication
contexts
Counts all items by ones
when items are perceived
Uses skip counting when all
groups are modelled
Uses known number facts
when all groups are modelled
Determines total by
skip counting
Uses known number
facts to determine total
Division contexts
Shares by ones when items
are perceived
Shares in groups using skip
counting when modelling
Uses known number facts to
determine total
Determines total by
skip counting
Uses known number
facts to determine total
Partitions
2s
Growth Points
3s
4s
5s
1. Count all (multiple
groups)
Gervasoni, A. (2010) EMU Program Template 6.1
10s
2s
3s
4s
5s
10s
2s
3s
4s
5s
2. Modelling multiplication & division when all items
are perceived
75
10s
2s
3s
4s
5s
10s
3. Abstracting multiplication & division when all
items are not perceived
EMU Program Templates
Counting & Place Value
M
T
W
T
F
Rich Activities focusing on Pattern, Addition & Subtraction, Multiplication & Division, and Measurement Contexts
M
T
M
T
M
T
W
T
F
T
F
T
F
Reflection
W
Home Activities
Gervasoni, A. (2010) EMU Program Template 6.2
W
76
EMU Program Templates
Insights and difficulties experienced by the child and his/her response to the assistance
program
Week Beginning;
_____________________
Name:
Name:
Name:
Name:
77
Gervasoni, A. (2010) EMU Program Template 6.3
EMU Program Templates
Insights and difficulties experienced by the child and
his/her response to the assistance program
Week Beginning;
_____________________
Gervasoni, A. (2010) EMU Program Template 6.4
78
EMU Program Templates
Extending
Mathematical
Understanding
Name:_____________________________________________________
79
Gervasoni, A. (2010) EMU Program Template 6
EMU Program Templates
STUDENT EMU MATHS BOOK
Date
Gervasoni, A. (2010) EMU Program Template 8
Today in EMU Maths I learnt…..
80
Gervasoni, A. (2010)