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_________Knowledge Stages: Name Forward Number Word Sequence (without dropping back) Start counting from one. I will tell you when to stop. (stop at 32) What’s the next number after? 5 9 13 19 12 29 46 69 80 99 139 209 899 2400 3049 603 000 989 999 Date each stage as it is achieved. Stage 0 15 Backward Number Word Sequence (without dropping back) Count backwards from 10. I will tell you when to stop. (stop at 0 or 1) Count backwards from 24. I will tell you when to stop. (stop at 11) What number comes before? 3 9 5 8 16 20 17 11 13 31 47 70 236 840 2400 3049 603 000 989 999 Numeral Identification What is this number? 3 9 5 1 8 6 0 13 19 11 16 12 66 43 Does not say FNWS up to 10. Stage 1 Stage 2 Stage 3 Says FNWS up to 10 Says FNWS up to 10 and number after. Says FNWS up to 20 and number after. Stage 0 Does not say BNWS up to 10. 2 38 7 137 Stage 5 Stage 6 Says number after up to 1 000. Says number after up to 1 000 000. Stage 1 Stage 2 Stage 3 Stage 4 Says BNWS back from 10 Says BNWS back from 10 and number before. Says BNWS back from 20 and number before. Says number before up to 100. Stage 5 Stage 6 Says number before up to 1 000 Says numberbefore up to 1 000 000 680 Stage 0 4 80 Stage 4 Says number after up to 100. 10 702 Place Value Tell me the answer to… Here are 4 dots. Here are ten more dots. How many dots are there now. 14,24,34,44,54 A toy costs $80. How many $10 notes do you need to pay for it? A radio costs $230. How many $10 notes do you need to pay for it? What number is the arrow pointing to? How do you know? You have $26 700 in $100 notes. How many notes do you have? What number is three tenths more than 4.8? How do you know? How many tenths are in all this number? 4.67 Put these decimals (0.39, 0.478, 0.8) in order from smallest to largest. How many hundredths are in all of this number? 2.097 Round 7.649 to the nearest tenth. Give three numbers between 7.59 and 7.6. If you had time how many numbers could you find? Name 137.5 % as a decimal Basic Facts Tell me the answer to… 2+3 5+4 6+ makes 10 6+6 9+9 10+4 7+10 8+6 6+9 8x5 5x7 17-9 15-6 6x7 8x4 567 639 Name all the factors of 81 What is the highest common factor of 72 and 81? What is the least common multiple of 8 and 12? Knowledge Questions from Numeracy Project Assessment (NumPA) Forms A, B & C Stage 1 Emergent numeral Iden. Identifies numerals to 10 Stage 0-1 Stage 3 Stage 4 Cannot count the number of objects. Uses 5 as a counting unit e.g., 5, 10, 15. Student uses 10 as a counting unit Stage 2 Identifies numerals to 20 Stage 5 Knows tens in numbers to 1 000 Uses tenths as a counting unit. Stage 2 Stage 3 Identifies numerals to 100 Stage 4 Identifies numerals to 1 000 Stage 6 Stage 7 Stage 8 Knows hundreds in numbers to 100 000 Recognises that ten tenths make one Knows tenths in, numbers with two decimal places. Orders decimals to three places Know, hundredths in decimals and rounds numbers to nearest tenth. Identify decimals between others and name a percentage as a decimal and vice versa. Counts the objects by one. Stage 0-1 Does not recall facts to 5 Stage 2 Recalls facts to 5 Stage 3 Recalls facts to 10 Stage 4 Stage 5 Recalls doubles and teen facts to 20 Recalls addition basic facts and multiplication facts for 2, 5, 10 Stage 6 Recalls subtraction and multiplication basic facts. Stage 7 Recalls division facts and names all factors of numbers to 100. Stage 8 Can name common factors of two numbers to 100 and least common multiple of numbers to 10. Strategy Stages: Individual Assessment Sheet. Name Addition and Subtraction Please get 8 counters for me (Unable to count. Stage 0 ) Work out 4 + 3 on materials (Unable to join sets. Stage 1) (Joins using materials. Stage 2) Date each stage as it is achieved. Comment where necessary. Stage 0 Stage 1 Stage 2 Stage 3 Stage 4 EmergentDoes not count up to 10 objects. Counts one to one. Counts from One on Materials. Counts from One by Imaging. Advanced CountingCounts on (Yes using imaging move on to task 3) Find 8 + 5 = (No. Stage 3) (Yes by counting on or part-whole move on to task 4) Find 9 + 8 = ((Yes by counting on. Stage 4) (Yes by part-whole strategy move on to task 5) Find 37 – 9 = (No, or Yes, by counting back. Stage 5) (Yes by part-whole strategy move on to task 6) Find 53 – 26 = (No. Stage 5) (Yes by part-whole strategy move on to task 7) Find 394 + 79 = (Regardless of answer, proceed to task 8) Find $403 – $97 = (If student solves 2 or 3 of tasks 6 - 8 correctly using different part-whole strategies rate at Stage 6. Otherwise rate at Stage 5) Multiplication and Division Here is a forest of trees. (Cover as described) How many trees in the forest altogether. (Uncover if unable to solve) If I planted 15 more trees how many rows of 5 would I have? Stage 2-3 Counts from One Counts all the objects Stage 4 Advanced Counting Uses skip-counting (Yes by counting all objects. Stage 2-3) (Yes by skip counting. Stage 4) (Yes by forming the factors where they have a known multiplication fact or by using repeated addition. For example, for 5 x 8: 5+5=10, 10+10+10+10=40. Move onto questions 2 and 3) Stage 5 Early Additive Part-Whole Derives addition and subtraction facts Stage 5 Stage 6 Early Additive Part-Whole Forms factors, uses known multiplication facts and repeated addition. Advanced Additive Part-Whole Derives multiplication facts. Stage 6 Advanced Additive Part-Whole. Uses at least two different advanced mental strategies. Stage 7 Advanced Multiplicative Part-Whole Uses at least two different advanced mental strategies. What is 3 x 20? If 3 x 20 = 60, what does 3 x 18 equal? What is 5 x 8? If 5 x 8 = 40, what does 3 x 16 equal? (No. Rate at Stage 4 or 5) (Yes by solving multiplication problems by deriving from known multiplication facts, for example, 3x20 = 60 so 3x18 = 60 – (3x2)=54. Move to Question 4) There are 24 muffins in each basket. How many muffins? At the car factory they need 4 wheels for each car. How many cars could they make with 72 wheels? Does the student use: (place value partitioning 6x20=120, 6x4=24, 120+24=144 or 40 4=10, 72-40=32, 324=8,10+8=18 (tidy numbers 6x25=150,150-6=144 or 804=20 so 724=20-(84)=18) (proportional reasoning and reversing 9x8=72 so 18x4=72 (doubling and halving)so 72 4=18(reversing) (No the student does not solve 4 or 5 correctly using at least 2 different advanced strategies. Rate at Stage 6. (Yes the student solves 4 or 5 correctly using at least 2 different advanced strategies. Rate at Stage 7. Proportions and Ratios Which of these cakes has been cut into thirds? (Indicate if unsure). Here are 12 jelly beans to spread out evenly on top of cake. You eat one third of the cake. How many jellies do you eat? (Unequal sharing. Stage 1) (Equal sharing physically/imaging. Stage 2-4) What is ¾ of 28? (Yes with addition facts, e.g. 1/3 of 12 as 4+4+4. Stage 5) (Yes using a combination of addition and multiplication facts, e.g. ¾ of 28 as ¼ of 20 is 5 so ¼ of 24 is 6 so ¼ of 28 is 7, or 1 /2 of 28 is 14, ½ of 14 is 7, 14 + 7 = 21. Stage 6) 12 is 2/3 of a number. What is the number? (No. Rate at Stage 5 or 6 based on above response. (Yes using multiplication and division. Rate at Stage 7 at least. Proceed on) It takes 10 balls of wool to make 15 beanies. How many to make 6 beanies? There are 21 boys and 14 girls in Ana’s class What % are boys? Does the student use: (Part-whole based on equivalent fractions such as finding relationships between different units, for example, 10 15 so 11.5 so 46 (unit fractions) or 6 x 2 ½ =15 so x2 ½=10 or 217=3, 147=2 common factor or finding relationships within the same units, e.g. 35x3=105 s0 21x3=63 and adjust 63 down to 60%. (Yes the student uses part-whole strategies successfully for both questions. Rate at Stage 8) Stage 1 Unequal Sharing Unequally shares objects. Stage 2-4 Equal Sharing Shares objects physically or by imaging Stage 5 Stage 6 Stage 7 Early Additive Part-Whole Uses addition facts Advanced Additive Part-Whole Uses addition, multiplication and division facts. Advanced Multiplicative Part-Whole Finds fractions of numbers using multiplication and division Stage 8 Advanced Proportional Part-Whole Uses at least two different advanced mental strategies.