Solve the following problems: 6. Name the shape. 7. Expand 64359 using powers. ACTIVITY TWO: 1. Multiply 536 by 23 using the lattice method.

The shape is a quadrilateral (4 sides). It has one pair of parallel sides (the top and bottom sides). It also has two right angles.

A quadrilateral with exactly one pair of parallel sides is a trapezoid (or trapezium). Since it also has two right angles, it is a right trapezoid.
The shape is a $\boxed{\text{Right Trapezoid}}$.

7. Expand 64359 using powers.

$64359 = 60000 + 4000 + 300 + 50 + 9$

The expanded form is $\boxed{6 \times 10^4 + 4 \times 10^3 + 3 \times 10^2 + 5 \times 10^1 + 9 \times 10^0}$.

ACTIVITY TWO

1. Multiply 536 by 23 using the lattice method.

Carry over any tens to the next diagonal sum.

• Rightmost diagonal: 8
• Next diagonal: $2 + 1 + 9 = 12$ (write 2, carry 1)
• Next diagonal: $6 + 0 + 5 + 1 (\text{carry}) = 12$ (write 2, carry 1)
• Next diagonal: $0 + 1 + 1 (\text{carry}) = 2$
• Leftmost diagonal: 1

The product is $\boxed{12328}$.

2. Shade the following
Note: No diagrams are provided, so the instructions for shading are given.

a) A - B
To shade $A - B$ (also written as $A \setminus B$), you would shade the region that contains all elements that are in set A but are not in set B. In a Venn diagram with two overlapping circles A and B, this means shading only the part of circle A that does not overlap with circle B.

b) (M $\cap$ K)'
To shade $(M \cap K)'$, you would shade the complement of the intersection of sets M and K. This means shading all elements that are not in the intersection of M and K. In a Venn diagram with two overlapping circles M and K, this means shading everything except the region where M and K overlap. This includes the parts of M and K that do not overlap, and any region outside both circles within the universal set.