8/14/2019 PV Teach 1.6 Ans

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Teacher Administration and Notes on the AnswersIf the tests are administered orally questions normally will be read to students then they can lookat the questions ,and write their answers. However some questions should not be read aloud

because this would make the answer easier. Such questions are indicated with an asterisk and anote not to read it aloud.

Place Value - 2/9Except for question 5 these questions do not require knowledge of operations with whole

numbers. Therefore they assess the most basic understanding of the place-value system.

1 In 635 the 3 stands for 3 TENS. In 367 the 3 stands for 3

This item assesses whether students recognise the names of the PV column in which digits appear.

2 Write six hundred and two as a number. Answer:

This item assesses whether students know how to insert relevant zeroes. (However, a correctanswer it does not necessarily mean the students fully understand the significance of the zero inthe place-value system.)

3*

(Don't read fifty or 70 aloud.)Which is bigger? Fifty or 70. Answer: The reason this item should not be read aloud is that some students will not know that fifty and 5tens are the same, and also not know that 70 means 7 tens; to compare fifty and 70 students need toknow compare 5 tens with 7 tens.

4 5 tens + 7 hundreds = 750. Fill in the spaces:7 ones + 6 hundreds = ........................ 9 hundreds + 4 tens = .........................The problems are deliberately given in words and out of the order usual of hundreds, then tensthen ones. This provides much more insightful information than a problem like 800 + 9 that can bedone by rules without understanding place-value.

5*

(Don't read the question aloud.) Take away one hundred from 695. Answer: This problem assesses whether students understand the equivalence of the word form and thecompact digit form of numbers. Also it assesses whether students realise that subtracting onehundred only requires removing 1 from the hundreds column in 695.

Place Value - Years 4/9

Except for question 5 these questions require knowledge of the place-value system applied toaddition and subtraction with whole numbers.

1* (Don't read the question aloud.) Fill in the space: 54 + sixteen = .............. tens

This problem is designed to see whether students understand that sixteen means one ten and 6

ones, and when this is combined with 54 this leads to 7 tens. The answer 70 is a very commonmistake. This helpss to assess whether students understand whether 70 and 7 tens are the same.

2 Donald buys a shirt that costs $65. He pays for it with a hundred dollar note. How

much change does the shopkeeper give Donald? Answer: ..

This problem is an advanced additive one. Methods of solution will require the students to knowthat 5 ones + 5 ones is one ten, or one ten minus 5 ones is 5 ones, and that ten tens is one hundred.A mixture of the number 65 in digit form and one hundred in words is designed confuse thosestudents who do not understand place value, and try to use an algorithm.

3 Write six thousand and eighty as a number. Answer: ..

This problem helps detect which students have a poor understanding of the significance of thezeroes in the place-value system.

8/14/2019 PV Teach 1.6 Ans

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4 Write down two numbers that are between 34 thousand and 35 thousand. Answer:

.. and ...

(Originally this problem asked for only one number. Answers like 34 000.5 and 34 500 suggested

these students were having difficulties in really understanding. So the question) This problem

helps detect the rote learners who have a rule for inserting a number between 34 000 and 35 000,but do not understand why it works. Here is an actual student answer: If counting normally itwould be the same number, so there is no number between 34 and 35."

5 You have $784.70 in your savings account that you withdraw in ten dollar notes, andcoins. What is the maximum number of ten dollar notes that you can get?70 78 79 80

Place Value - 6/9These questions require knowledge of the place-value system applied to multiplication anddivision with whole numbers.

1 How many hundred dollar notes are needed to make a pile of money worth seven

thousand six hundred dollars?Answer: .

This helps test whether the students understand the basic multiplicative place-value idea thatthat ten hundreds are interchangeable with one thousand.

2* (Don't read the question aloud.) 1 000 045 - = 999 999. What is the number that

goes in the box? Answer:

This advanced additive problem is designed to see whether students understand that adding 1 tolarge numbers like 999 999 roll the number over to 1 000 000. So the answer is 1 + 45 = 46.

3* (Don't read the question aloud.) 99 987 + = 100 003. What is the number

that goes in the box? Answer:

Again the roll-over effect is being tested. Here adding 13 produces 100 000. So the answer is

13 + 3 = 16

4 Divide two thousand and fifty by ten. Answer: .

Again words are used to try to confuse the student who is algorithmic. Here two thousand divided

by ten is two hundred, and fifty divided by ten is five ones. So the answer is 205.

5 What does 999 x 9 equal? Answer:

This item assesses students' knowledge of the distributive law, which is the core idea required in

multiplicative thinking. Here 999 x 9 = 1000 x 9 - 1 x 9 = 9000 - 9 = 8991.

6 Ring the two correct numbers. Which two numbers multiplied together give an

answer closest to the target number 1980? 50 30 20 40

This item tests estimation. The only numbers when multiplied that are anywhere near 1980 are 50and 40.