Grade 5 – Operations and Algebraic Thinking
1. A chocolate box has 3 trays of chocolate with 12 chocolates in each tray. Write an equation to
represent the total number of chocolates in the box.
A chocolate “Crate” has 5 trays. Each Tray is a Rectangular grid with 6 rows and 10 columns.
Write an expression for the number of chocolates in a crate.
2. What numbers can you make with 1, 2, 3, and 4 using the operations of addition, subtraction,
concatenation of digits and multiplication? For example, we can write 15 as
15 = (3×4) + 1+2.
We can write 144 as
144=(3x4)x12
You can use parentheses as many times as you like but each of the numbers 1, 2, 3, and 4 can
be used at most once and no other digits are allowed. Find all the ways to make 27. What is
the smallest positive integer that cannot be made? What is the largest integer that can be
made? What is the smallest integer (i.e. negative) that can be made?
3. True or False? Explain. 2 x (9 +7) = (9 +7) + ( 9 +7)
4. True or False? Explain. 67 + 86 = 68 + 85
5. True or False? Explain. 41+36=13+64
6. True or False? Explain. 52+47=24+75
7. Find digits a,b,c,d all different(not the same as above) so that ad+bc=db+ca
8. Find digits a,b,c,d all different(not the same as above) so that ad+bc≠db+ca
9. Find the blank value as simply as possible. Explain. 43+ ___= 48 + 76
10. Solve for m - Explain m+m+m = m+12
11. Insert parenthesis to make the following statements true
(a) 4 +7 x 3 = 33 (b) 4 +7 x 3 = 25 (are parenthesis needed?)
(c) 4+3x5+2=21 (d) 4+3x5+2=37 (e) 4+3x5+2=25 (f) 4+3x5+2=49
12. By inserting zero, one or two pairs of parenthesis, list all the numbers you can make from
6 +5 ÷ 5-2. List the numbers from smallest to largest. Repeat this for 7+4÷4-3. What number
is the same in the two lists?
13. Compute the following using the Order of Operations 60 +15÷3-6. Change the numbers
60,15,3 and 6 (but not the operations) so that these all become different and yet we get the same
answer. Repeat for 4 x 5 + 3 – 2 ÷ 2
14.
Above top we show a special huge seating table where there are 8 students on
the inside and 16 on the outside. How many seats will there be with the
configuration shown at bottom where we line up two rows of 20 huge tables as
shown. Note that where the two rows touch there are no seats and there are no
seats internal to each row where the huge tables touch.