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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 1120 (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. 4355 (error sequence) ______________________________ b. 7893 (error sequence) ______________________________ c. 95122 (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. 100 (error sequence) ______________________________ b. 2210 (error sequence) ______________________________ c. 5448 (error sequence) ______________________________ d. 9488 (error sequence) ______________________________ e. 114108 (error sequence) ______________________________ f. 124118 (error sequence) _____________________________ 11. Counting by Tens 0120 (error sequence)________________________________ 12. Counting by Fives 0110 (error sequence)________________________________ 13. Counting by Twos 040 (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 43 Chapter 6 EMU Templates 62 Gervasoni, A. (2010) Extending mathematical understanding specialist teacher manual (2nd Ed). Ballarat: Ballarat Heritage Services 63 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 66 67 Gervasoni, A. (2010) EMU Program Sample 1 Chapter 6 Gervasoni, A. (2010) EMU Program Template 1 68 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 05 010 015 05 010 015 050 090 0120 210 220 240 5 6 7 8 9 020 030 035 020 025 030 100 200 300 520 550 5100 1/1 corresp. 500 900 1200 1050 1090 10120 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 10 015 019 2029 2049 5099 100999 Writing 1 2 3 4 5 6 7 8 9 10 015 019 2029 2049 5099 100999 Ordering 02 04 06 08 010 015 019 2029 2049 5099 100999 Partitioning and Interpreting 02 04 06 08 010 015 019 2029 2049 5099 100999 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 010 019 029 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 0120 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 050 100 500 Growth Point 3. Count forwards & backwards by ones, from any starting point 090 200 900 0120 210 220 300 520 550 1200 1050 1090 240 5100 10120 xy 10s 4. Skip count by 2s, 5s & 10s 2s 5s 2s 6s 9s xy 4s 8s 5. Skip count by 2s, 5s & 10s from any number. 3s 7s xy 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 015 019 2029 2049 5099 100150 100199 200299 200499 500999 10003000 Writing 015 019 2029 2049 5099 100150 100199 200299 200499 500999 10003000 Interpreting 015 019 2029 2049 5099 100150 100199 200299 200499 500999 10003000 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 0120 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)