Unit 5
Big Number, Estimation, and Computation
Unit 5 begins with two lessons that focus on extending multiplication
skills, in preparation for the introduction of the partial-products algorithm
for multiplication. The lattice algorithm is also introduced as an
alternative to the partial-product algorithm. This unit also emphasizes
reading, writing, and using large numbers, including the use of powers of
10 to represent large numbers. Unit 5 has four main areas of focus:
 To extend basic multiplication facts and to review the basic
principles of multiplication of multidigit numbers,
 To provide practice estimating and deciding when estimation is
appropriate,
 To review and provide practice with the partial-products algorithm
and the lattice method for multiplication, and
 To provide practice reading, writing, and comparing large numbers
using patterns in the base-ten place-value system.
Vocabulary
Billion – 1.000,000,000 or 109; 1,000 million
Estimate – A close, rather than exact, answer; an approximate answer to a
computation.
Exponent – A small raised number used in exponential notation to tell how
many times the base is used as a factor. For example, in 53, the base is 5, the
exponent is 3, and 53 = 5 * 5 * 5 = 125.
Exponential Notation – A way to show repeated multiplication by the same
factor. For example, 23 is exponential notation for 2 * 2 * 2. The small
raised 3 is called the exponent. It tells how many times the number 2, called
the base, is used as a factor.
Extended Multiplication Fact – A multiplication fact involving multiples
of 10, 100, and so on. In an extended multiplication fact, each factor has
only one digit that is not 0. For example, 400 * 6 = 2,400 and 20 * 30 = 600
are extended multiplication facts.
Lattice Multiplication – A very old way to multiply multidigit numbers.
(See Student Reference Book, page 19 for further explanation and examples.)
Magnitude Estimate – A rough estimate of whether a number is in the 1s,
10s, 100s, 1,000s, and so on.
Million – 1,000,000, or 106; 1,000 thousand.
Partial Products Multiplication – A way to multiply in which the value of
each digit in one factor is multiplied by the value of each digit in the other
factor. The final product is the sum of the partial products. (See Student
Reference Book, page 18 for further explanation and examples.)
Power of 10 – A whole number that can be written as a product using only
10s as factors. For example, 100 is equal to 10 * 10, or 10 2. 100 is 10 to the
second power or 10 squared.
Round a Number - To approximate a number to make it easier to work with
or to make it better reflect the precision of the data.
Games
Beat the Calculator – Student Reference Book, page 233
The purpose of this game is to sharpen mental multiplication skills and solve
extended multiplication facts.
Multiplication Wrestling – Student Reference Book, page 253
This game will give students practice at calculating and finding the sum of
partial products.
Product Pile-Up – Student Reference Book, page 259
The goal of this game is to develop automaticity with multiplication facts.
Name That Number – Student Reference Book, page 254
Playing this game will help students practice representing numbers in
different ways.
High-Number Toss – Student Reference Book, page 252
Identifying values of digits and comparing large numbers is the goal of this
game.
Web Sites
This tic tac toe is a good one for reviewing all the math operations on
various levels:
http://www.funbrain.com/tictactoe/index.html
This place value puzzle game is a good one for practice in rounding:
http://www.funbrain.com/tens/index.html
This is site does a good job of explaining lattice multiplication:
http://www.coolmath4kids.com/times-tables/times-tables-lesson-latticemultiplication-1.html
Do-Anytime Activities
To work with your child on concepts taught in this unit, try these interesting
and rewarding activities:
 To help your child practice handling big numbers, have him or her
lookup the distances from Earth to some of the planets in the solar
system, such as the distance from Earth to Mars, to Jupiter, to Saturn,
and so on.
 Have your child look up the box-office gross of one or more favorite
movies.
 Help your child look up the populations and land areas of the state and
city in which you live and compare them with the populations and
areas of other states and cities.
 Have your child locate big numbers in newspapers and other sources
and ask him or her to read them to you. Or, you can read the numbers
and have your child write them.