 Math Unit 2

Study Guide

Chapter 1:

·      The following are strategies taught for adding mentally.  If a student struggles with adding mentally, they are encouraged to borrow when subtracting and carry when adding.

·      Mental Math strategies for addition

·      Mental Math strategies for subtraction

o   483-98

o   Round 98 to 100

o   Subtract 100 from 483

o   Add the two from rounding 98 to 100

o   This can all be done “mentally”

·      Mental Math strategies

o   Find groups of ten in the ones column to assist in “mentally” adding these numbers

·      Examples of test questions:

o   16 + ___ = 52

o   470 + 71 = ___

o   Add 74 and 5. ____

o   What number is 9 more than 23? _____

o   What is 55 + 31? ____

o   Show the value of 56 + 87 + 13 + 42?

o   Subtract 43 from 88. ____

o   Subtract 6 tens from 80. ___

o   873-298 = ____

Chapter 2:

·      Understanding sum (+) and difference (-)

o   Students learn to relate addition and subtraction to the part-whole concept and use subtraction to compare two sets of objects using subtraction

o   When finding a sum, students add

§  If you have three blue and two red, how many do you have?

§  2+3=5

 Blue Blue Blue Red Red

o   When finding a difference, subtract

§  How many more blue than red?

§  5-3=2

 Blue Blue Blue Blue Blue

 Red Red Red

o   60-34=

·      Part-whole models

o   Using one bar

o   What is the total?

 21 9

·      Comparison models

o   Using two bars

o   The total is 21.  If one bar is 9, what is the difference?

 21

 9 ?

·      Sum and difference – greater or smaller than

o   Find the answer on each side of the equation.  Then fill in the comparison symbol.

o   10-2 ___ 10-3

o   10-2 > 10-3

·      Examples of test questions:

o   What is the sum of 8 and 5?

o   Find the sum of 58 and 14. ___

o   24 more than 89 is ___.

o   86 + ___ = 91

o   Find the difference between 13 and 78. ___

o   The sum of two numbers is 73.  One number is 32.  The other number is ___.

o   45 less than ____ is 20.

o   ____ - 33 = 64

o   Compare the two numbers 78 and 34.

§  Which is smaller? ___

§  ___ is ____ more than ____

o   Fill in + or -

§  54 ___ 33 =  87

§  26 ___ 42 < 60 ___ 28

o   Fill in >, <, or =

§  63 + 99 ___ 84 – 34

§  55 + 4 __ 67 – 24 ___ 88 - 15

Chapter 3:

·      Estimation

o   Exact: 6326+4608=10,934

o   Estimation of the above problem: 6,000+5,000=11,000

·      Examples of test questions:

o   Find the sum of 63 and 58.  Use estimation to check if your answer is reasonable.

§  There is a separate box to work out the estimation problem from the actual problem on this test.  There will also be a question on most problems that asks “Is your answer reasonable?”

o   Estimate the difference between 935 and 826.  The answer should be about ______.

o   What is 481 + 293 + 602?  Use estimation to check if your answer is reasonable.

o   What is 43 more than 826? ___  Is the answer closer to 800 or 900? ___

o   Frank did the following estimation.  900-700=200

§  The question was 8__3 – 713.  What could the number on the line be?

o   Find the actual value of the following.  Use estimation to check if your answer is reasonable.  82 + 61 + 29 + 38 = ___

o   Fill in the blank with the missing number.  Use estimation to check if the answer is reasonable.  772 - ____ = 651

o   Sally has \$290.  Frank has \$702 more than Sally.  Estimate the amount Frank has.

o   Estimate the sum of 713 and 634 by rounding each number to the nearest hundred.

o   Brad did the addition problem 152 + 88 = 281.  Round 152 to the nearest hundred and 88 to the nearest ten.  Then use estimation to check if his answer is reasonable.

Chapter 4:

·      Word problems: use the model drawing examples sent home at the beginning of the year.

o   Model Drawing Step by Step song (to the tune of “Row, Row, Row Your Boat”).

Merrily, Merrily, Merrily, Merrily; Write it as an answer

Who, Who, Who’s involved; Write it on the left

What, What, What’s involved; Write it underneath

Draw, Draw the unit bars; Gently on the right

Chunk, Chunk, Chunk the problem; Adjust the unit bars

Think, Think, Think, Think; Write the question mark

Work, Work the computation; Gently to the side

o   Six Steps for Model Drawing

§  Read the entire problem.  Underline the question.

§  Write a complete sentence to answer the question at the bottom.

§  Identify the “who” and the “what” – called the variables.

§  Draw a unit bar to model each variable (each who/what).

§  Chunk the problem and adjust the unit bars to match the information.  Fill in the question mark (but don’t erase it).

§  Work the computation and show all your work.

·      Examples of test questions.  Solve the following word problems.

o   82 pickles were eaten.  77 more pickles were eaten.  How many pickles were eaten altogether?

o   77 pickles were in a can.  34 pickles were eaten.  How many pickles were left?

o   Will has \$591.  He has \$72 more than Jade.  How much does Jade have?

o   Sam won 831 tickets.  He lost 502 tickets.  How many tickets did he have left?

o   Brenna sold 42 cakes on Monday, 41 on Tuesday, 80 on Wednesday and 2 on Thursday.  How many did she sell altogether?

o   There are 614 boys and 302 girls at the concert.  How many students?  There are 33 more parents than students.  How many parents?

o   David has 109 apples.  Alex has 39 more apples.  How many apples does Alex have?  How many do they have altogether?

o   Bridget has 52 envelopes.  She used 48.  How many are left?  She will need 69 more envelopes for letters.  How many more envelopes will she need?

o   Sherry gave away 521 sweet and had 132 left.  How many did she have at first?  If she gave away 94 another day, how many does she have left?

o   Frank had to make 64 meals.  He made 43 for breakfast and 15 for lunch.  How many did he make altogether?  How many did he have to make for dinner?

Chapter 5:

·      Adding ones, tens, hundreds and thousands (carrying)

o   2,803+1,443=4,246

·      Renaming three times

o   3,589+2,443=6,032

·      Examples of test questions:

o   Find the sum of 908 and 13.

o   What is the sum of 908 and 13?

o   What is 13 more than 908?

o   Write the missing digit.

239

+4?

286

o   Round 2,392 and 6,913 to the nearest hundred.  Add.

o   Know how to check if a problem is correct.  If subtracting, add.  If adding, subtract.

2,392

+6,913

9,305

check the problem:

9,305

-6,913

2,392

o   Form the greatest and smallest 4-digit numbers using each digit only once.

Chapter 6:

·      Subtracting ones, tens hundreds and thousands (borrowing)

o   3,246-1,634=1,612

·      Renaming four times

o   5,243-2,787=2,456

·      Subtracting from a whole thousand

o   5,200-948=4,252

·      Examples of test questions:

o   Subtract 3 from 702.

o   Subtract 5872 from 8321.

o   What is 33 less than 1,562?

o   How much was sold if there were 579 originally and 412 were left?

o   Write in the missing digit(s):

2?9

+47

286

6,2?9

+ ?47

6,486

o   Know how to check if a problem is correct.  If subtracting, add.  If adding, subtract.

9,305

-6,913

2,392

check the problem:

2,392

+6,913

9,305

o   Be able to estimate numbers to see if answers are reasonable.  Be able to round to tens, hundreds, and thousands.

§  345-281 = 64

§  estimate: 350-280 = 70

§  This is a reasonable answer.

o   How many more apples than oranges are there, if there are 492 apples and 399 oranges?

o   Frank won \$569.  He won \$64 more than Ed.  How much did Ed earn?

o   Two numbers were rounded to check if the difference was reasonable.

§  5000-3000 = 2000

§  What were the original numbers?  Choose from the following possibilities: 3,891   2,743   4,001   5,352   3,891

§  Find the difference of the original numbers

o   The History book has 54 pages.  The Science book has 312 pages.  The Latin book has 1,290 pages.  How many more pages are in the Latin book than the Science book?  How many fewer pages are in the History book than the Latin book?

Chapter 7:

·      Two-step word problems

o   Questions to guide discussion:

§  What information is provided in the task?

§  What is it that needs to be worked out?

§  Which model should be drawn?

§  Is a total given?

§  Are any parts given?

§  Are the two parts given?

§  What part is given?

§  Which part is larger?

§  Are there two parts to be compared?

§  What are the two parts that are being compared?

§  Which is the larger part?

·      Examples of test questions:

o   Sam has 123 pencils.  74 are mechanical, 45 are #2 pencils, and the rest are colored pencils.  How many colored pencils are there?

o   Sherry put \$467 in her savings account on Monday.  On Tuesday, she put in \$123 more than Monday.  On Wednesday, she put in \$63 more than Tuesday.  How much did she put in altogether?

o   There were 7 squirrels in the tree.  There were 9 more squirrels than birds.  There were 4 fewer chipmunks than birds.  How many chipmunks were there?

o   Frank has \$2,304.  How much is left if Frank spends \$456 on groceries and \$672 on food?

o   Frank has \$2,304.  He spent some money and had \$902 left.  He earned \$44 and spent it all.  How much did he spend altogether?

o   Archie ate 412 grapes.  He ate 43 more grapes than Ellie.  How many grapes did they eat altogether?

o   The restaurant bill came to \$698 for the meal and beverages.  \$562 was for the meal.  How much were the beverages?  How much more was the meal than the beverages?

o   A word problem and solution are shown.  Be able to round the numbers to check if the answer is reasonable.

§  Word Problem

·      Frank has \$2,304.  He spent \$902 on Monday and \$328 on Tuesday.  How much did he have left?

§  Solution

·      \$2,304-\$902 = \$1,402

·      \$1,402-\$328 = \$1,074

§  Round:

·      2,000-900 = 1,100

·      1,000-300 = 700