Download test - The Common Denominator Program

The Common Denominator Program - Y1 Skills Check
Part One
1. Find the sum using the standard algorithm:
4678
3912
1156
+8609
2. In the following addition question, what does the 1 above the 312 mean conceptually?
1
121
+698
819
3. Find the difference using the standard algorithm:
10027
−8639
4. Use the take away model to give a visual representation of the statement 7 − 3 = 4.
5. Find the product using the standard algorithm:
748
×596
6. Give a visual representation of the statement 11 ÷ 5 = 2R1 using
(i) the repeated subtraction (measurement) model for division.
(ii) the fair share (partitive) model for division.
7. Using the standard algorithm, find the quotient and remainder when 57942 is divided by
19.
8. Explain briefly why the expression 5 ÷ 0 is undefined.
Part Two
1. Without using long division, answer the following:
(i) Is 6732 divisible by 3? How do you know?
(ii) Is 6732 divisible by 5? How do you know?
(iii) Is 6732 divisible by 6? How do you know?
(iv) Is 6732 divisible by 11? How do you know?
2. List the factor set, in pairs, for the following numbers:
(i) 56
(ii) 60
(iii) 89
3. List the first four multiples of 18.
4. Determine the greatest common factor of 56 and 60.
5. Determine the lowest common multiple of 18 and 27.
6. List all prime numbers between 40 and 60.
7. Find the prime power factorizations of the following numbers:
(i) 56
(ii) 100
8. The prime power factorization of a number is 17 × 112 × 2.
(i) Name one prime factor of the number.
(ii) Name two composite factors of the number.
(iii) How many total factors does the number have?
(iv) Is the number even or odd? How do you know?
Part Three
1. When solving the problem 8 × 3 + 2 = ?, a student writes
8 × 3 = 24 + 2 = 26
Explain what is incorrect in the student’s work, and what you might say to help the student
understand their misconception.
2. (30 × 40) + (30 × 5) + (9 × 40) + (9 × 5) = 39 × ?
3. Which operation is commutative and which is not? Briefly explain your answers.
(i) To put on your left shoe and to put on your right shoe.
(ii) To hang up the phone and to say goodbye.
4. Determine if the statement is true or false. If it is false, provide a counter-example showing
why it is false.
(i) The set of natural numbers (N) are closed under multiplication.
(ii) The set of natural numbers (N) are closed under subtraction.
(iii) The set of integers (Z) are closed under subtraction.
(iv) The set of integers (Z) are closed under division.
5. Provide an integer addition or subtraction statement for each visualization given below.
You may assume that the white chips are positive.
(i)
(ii)
6. Which expression below is equivalent to 3 − 1?
(i) 1 − 3
(ii) −1 + 3
(iii) 1 + (−3)
(iv) −1 + (−3)
7. Which expression is equivalent to (4 − 1) + 3?
(i) 4 − (1 + 3)
(ii) 4 + (1 − 3)
(iii) 4 + (−1 + 3)
(iv) 4 − (−1 − 3)
8. Simplify the following expression using the order of operations. Be sure to begin every new
step on a new line. You may use the relocation property as you see fit.
42 ÷ 9 ÷ 8 × 7 × 81 ÷ 7 − 32 × 42 ÷ 2 − 9 ÷ 13 × 3 × 26