MATH CHEAT SHEET REFRESHER COURSE ON ESTIMATION AND OPERATIONS Math at the elementary level revolves around learning concepts, understanding patterns, and the basic operations of addition, subtraction, multiplication and division. Unless you’re an accountant or a math teacher, you’ve probably forgotten the math lessons you learned in grade school. But that’s no excuse to shy away from helping your child. “It is important for a parent to know what their child is learning,” says Richard E. Bavaria, Ph.D., vice president of education for Sylvan Learning Center. “A parent who is wise and caring will know what her child is studying in school and will also be able to support her child during homework and test time.” Bavaria says that doesn’t mean a parent should be expected to be an expert in everything. “But it is important for a parent to know the teacher’s expectations and the major topics that will be covered,” he says. “This way, a parent can make a conscious effort to use these topics as often as possible in a daily routine.” Here’s the refresher course you’ve been waiting for. Estimation is a way to find an approximate answer, not an exact answer. Begin with making estimations about nonmeasured items. Have your child guess how many pennies, jelly beans or pebbles are in a jar. Compare guesses with actual amounts. Point out that larger jars contain more than smaller jars, and same-sized jars can hold fewer large items and more small items. Now move on to estimating measurements. Put units of measurement in perspective by using real objects. A paperclip is about 1 inch long. A small book is about 1 pound. Be sure your child is familiar with using rulers, measuring tape and scales. Try this exercise: Have your child estimate his height, then measure his actual height. Was the guess too big or too small? Subtract the bigger number from the smaller number to determine how close the guess was. Now have your child guess the height of other objects based on his own actual height. Are the guesses getting closer to the actual size? Use inequality symbols to show that two amounts are not equal. > greater than < less than ≥ greater than or equal to ≤ less than or equal to Operations Addition is the process of joining two or more numbers to create a larger single number.   5 11 17 124 4 + 3 = 7 +6 +14 +23 +239   —— —— —— ——   11 25 40 363 Subtraction is the process of taking a number away from a number to create a smaller single number.   15 81 137 390 8 - 2 = 6 -6 -33 -123 -239   —— —— —— ——   9 48 14 51 Multiplication is the process of adding a number to itself a given number of times.     5 12 32 4 × 3 = 4 + 4 + 4 = 12 3 × 9 = 27 × 3 × 4 × 12     —— —— ——     15 48 64         +320         ——         384 Division is the process of breaking down a number into a number of equal parts. 12 ÷ 4 = 3 5 ÷ 1 = 5 100 ÷ 10 = 10 Operations and estimations Rounding is a method for changing a large number into a simpler number. To understand rounding, think about decimal places. Each number can be broken down into decimal parts. For example: Think about the number 132 as 1 | 3 | 2. The 2 is in the ones place, the 3 is in the tens place and the 1 is in the hundreds place. The number 132 is actually 100 + 30 + 2, or (1 × 100) + (3 × 10) + (2 × 1). Round down a number less than 5. Round up a number that is 5 or higher. To round 132 to the nearest ten, look at the number in the ones place and round up or down. Because 2 is less than 5, round it down to 130. If the number is 135, you should round up to 140. Now try estimating answers to large problems by rounding to the nearest ten: 32 30 547 550 1,322 1,320 +69 +70 -389 -390 +2,589 +2,590 —— —— —— —— —— —— 101 100 158 160 3,911 3,910 Notice that the estimated answers are close to the actual answers. Rounding and estimation are ways to add or subtract large numbers without a calculator. Use multiplication to estimate how many items are in a set. Count the number of rows and the number of columns and multiply these numbers together to find the total number of items. Think of a carton of eggs. There are 6 rows and 2 columns or 6 × 2 = 12. For objects that have different sizes, such as books on a shelf, use the same method to get an estimation of how many items there are total. Next time you estimate a jar full of jelly beans, just count the number of beans you can see on the bottom. Then count how many layers and multiply these two numbers to get a very close estimate. By Matthew DeFour Worksheet: 1a. Look at a map of the United States. Which state is bigger: Montana or California? 1b. Which state is smaller: Indiana or Maine? 1c. Which city is closer to New York City: Boston or Washington, D.C.? Answer: Maine Answer: California Answer: Boston 2. Round the following numbers to the nearest 10   a. 18 20   b. 35 40   c. 129 130 3. Round the following numbers to the nearest 100   d. 933 900   e. 1,670 1700 3. Estimate the answers to the nearest ten: 37 1,230 78 + 19 = 100 123 + 209 = 330 +23 + 922     —— ——     60 2,150     4. Sarah checks out 5 books from the library. Each book weighs about 2 pounds. How much weight does she have to carry? Answer: 10 pounds 5. If a paperclip is 1 inch, and 6 paperclips are as long as one pen, how many inches long are 2 pens? Answer: 12 inches 6. A bookshelf has 3 rows. Each row is 48 inches wide. How many books will fit on the bookshelf if each book is about 2 inches wide? Answer: 72 Books