math mammoth grade 3-b complete worktext samples · chapter 6: place value with thousands...

Contents Chapter 6: Place Value with Thousands

Introduction ..................................................................... 5 Thousand and Beyond .................................................... 7More Practice with Place Value .................................... 11Which Number Is Greater ............................................. 16Mental Adding and Subtracting .................................... 19Adding and Subtracting in Columns ............................ 22Rounding to the Nearest Hundred ................................ 26Rounding to the Nearest Thousand .............................. 28Estimating Sums and Differences ................................. 30Review.............................................................................. 33

Chapter 7: Geometry

Introduction .................................................................... 35Shapes and Parallelograms ........................................... 38Right Angles ................................................................... 41Tilings .............................................................................. 46Line Symmetry .............................................................. 48Mirror Points ................................................................ 50Getting Started with Area .............................................. 52Perimeter ......................................................................... 55Three-Dimensional Figures ........................................... 57Geometry Review............................................................ 59

Chapter 8: Measuring

Introduction ................................................................... 60Measuring to the Nearest Fourth-Inch ........................ 62Centimeters and Millimeters ........................................ 67Feet, Yards and Miles ................................................... 71Measuring Length in the Metric System: Meters, Kilometers and More.......................................

73

Using Ounces .................................................................. 75Using Grams ................................................................... 80

3Sample worksheet from www.MathMammoth.com

Estimate Weight 2............................................................ 83Practicing with Units of Volume .................................... 84Millileters and Liters ...................................................... 87Measuring Temperature: Fahrenheit ........................... 89Measuring Temperature: Celsius .................................. 91Review .............................................................................. 93

Chapter 9: Division Introduction ..................................................................... 95Division as Making Groups ............................................ 97Division and Multiplication ............................................ 101Division and Multiplication Facts .................................. 105Dividing Evenly into Groups .......................................... 109Zero and One Division .................................................... 113When Division is not Exact ............................................ 117Checking Division with a Remainder............................. 121Fraction - Division Connection ...................................... 124Review of Division .......................................................... 126

Chapter 10: More on Multiplication Introduction ..................................................................... 128Multiplying by Whole Tens and Hundreds .................. 130Using All Four Operations ............................................ 134Multiplying in Parts ....................................................... 138Multiplying in Columns - the Easy Way ...................... 143Multiplying in Columns - the Easy Way, Part 2 ......... 146Review ............................................................................. 148

Chapter 11: Fractions Introduction ..................................................................... 149Understanding Fractions ................................................ 151Part of a Whole Group ................................................... 154Mixed Numbers .............................................................. 157Add and Subtract Like Fractions .................................. 161Decimal Numbers - Tenths ............................................. 164Fractions Review ............................................................. 166


Chapter 6: Place Value with Thousands Introduction

The sixth chapter of Math Mammoth Grade 3-B Complete Worktext covers 4-digit numbers (thousands). First we study place value. The emphasis is on trying to get familiar with numbers that have thousands and visualize them on a number line. Then we study addition and subtraction using these numbers.

The lesson about mental math stresses the similarities to adding or subtracting smaller numbers, which helps the student's understanding. Mental math also helps to build number sense. You can make more mental math worksheets using the worksheet maker on the CD.

Adding and subtracting in columns should be relatively easy now, assuming the student has grasped them well earlier, when studying 2-and 3-digit numbers. If your student needs more practice for these, don't hesitate to use the worksheet maker on the CD.

Then there are several lessons about rounding and estimating, which are very important skills needed in everyday life.

The Lessons

Helpful Resources on the Internet Base Blocks from National Library of Virtual Manipulatives Place enough thousand cubes, hundred-flats, ten-sticks, and one-blocks to the work area to show given numbers. Choose "Columns = 4" to restrict the program to four-digit numbers. http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html

Cookie Dough Practice naming big numbers. http://www.funbrain.com/numwords/index.html

page spanThousand and Beyond .............................................. 7 4 pagesMore Practice with Place Value ............................... 11 5 pagesWhich Number is Greater ........................................ 16 3 pagesMental Adding and Subtracting ................................ 19 3 pagesAdding and Subtracting in Columns ........................ 22 4 pagesRounding to the Nearest Hundred ............................ 26 2 pagesRounding to the Nearest Thousand .......................... 28 2 pagesEstimating Sums and Differences ............................ 30 3 pagesReview ...................................................................... 33 2 pages

5

http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html

http://www.funbrain.com/numwords/index.html

4. Write in normal form. Be careful! You need zeros a lot.

a.

9000 + 90 + 800 = ______

6000 + 7 = ______

6 + 7000 = ______

b.

1000 + 90 + 900 + 3 = ______

7000 + 80 + 9 = ______

7000 + 800 + 9 = ______

c.

5000 + 40 + 4 + 500 = ______

3000 + 50 + 900 + 5 = ______

2000 + 30 + 6 = ______

d.

4 + 9000 + 70 = ______

600 + 3000 + 5 = ______

10 + 200 + 3000 = ______

e.

5000 + 80 = ______

500 + 8000 = ______

4000 + 900 + 7 = ______

f.

400 + 9000 + 7 = ______

40 + 6000 + 500 = ______

80 + 500 + 8000 + 6 = ______

g. 2 thousand 7 ones 4 tens

h. 2 tens 6 hundred 4 thousand

i. 7 thousand 8 hundred 8 ones j. 5 thousand 6 tens

k. 3 thousand 4 ones

l. 5 hundred 9 thousand


3. Subtract. Check by adding.

4. Solve.

Subtract in Columns: 5139 – 2244

We can't subtract 4 tens out of 3 tens, so we need to borrow from the hundreds.

Now we can't subtract 2 hundreds out of 0 hundreds, so we need to borrow from the thousands. Complete.

Check by adding.

5 1 3 9

– 2 2 4 4

5

0

13

5 1 3 9– 2 2 4 4

5

0

13

5 1 3 9– 2 2 4 4

9 5

4

100

13

5 1 3 9– 2 2 4 4

9 5

+ 2 2 4 4

a. 5 0 9 1– 5 1 0

b. 2 9 1 3– 1 7 1 6

c. 8 4 0 2– 1 3 7 8

d. 6 8 8 1– 9 1 1

e. 6 5 4 6– 3 4 9 0

f. 9 0 8 0– 5 0 2 5

g. 4 5 0 9– 1 1 1 6

h. 6 2 0 9– 2 0 6 5

i. 7 1 8 2– 5 3 6 5

j. 4 0 3 7– 1 9 1 6

k. 1 1 7 3– 9 2 8

l. 7 1 5 4– 3 9 4 7

a. 4908 – 203 – 1420 b. 3924 + 291 + 2932 – 2910


Chapter 7: Geometry Introduction

The seventh chapter of Math Mammoth Grade 3-B Complete Worktext deals with some elementary geometry topics, such as parallel lines, right angles, shapes, area, perimeter and volume.

In the first lesson, the student reviews the names of various shapes, and learns about parallel lines and parallelograms in more detail.

Then, we study the concept of right angles in detail. The lesson is quite long, so you probably will cover it over several days. It shows how to draw perpendicular lines (lines at a right angle) using a protractor, or a triangle-shaped ruler, and lets the student practice drawing right angles or shapes that have right angles. In continuation, the lesson also shows how to draw parallel lines.

Tilings is a simple lesson that lets students also design their own tilings. Then follow lessons on symmetry, area, perimeter, and three-dimensional figures. Most of these are on the introductory level.

When studying three-dimensional figures, such as a cube, a rectangular prism, pyramids, a cone, and a cylinder, you can make models for them from the PDF printouts provided in the /cutouts/ folder. Just print them out, cut out the shapes, fold the sides, and glue or tape the figures together.

Alternatively you can buy them, usually made in plastic. Search on the internet for "geometric solids".

The Lessons page span

Shapes and Parallelograms ............................. 38 3 pagesRight Angles .................................................. 41 5 pagesTilings ............................................................ 46 2 pagesLine Symmetry ............................................... 48 2 pagesMirror Points ................................................. 48 2 pagesGetting Started with Area .............................. 52 3 pagesPerimeter ....................................................... 55 2 pagesThree-Dimensional Figures ........................... 57 2 pagesGeometry Review ......................................... 59 1 page

35

http://illuminations.nctm.org/ActivityDetail.aspx?ID=72

2. Complete these drawings so you get: a) a rectangle; b) a square.

3. Draw a line that is perpendicular to the given line and that goes through the point.

4. Draw here any triangle that has a right angle. It is called a right triangle. (Hint: Start by drawing the right angle.)

a. b.


Line Symmetry

1. Are these figures symmetrical? Draw a symmetry line to those that are. You can also cut them out and fold them to check.

These figures are symmetrical in relation to the dashed line. The line is called a symmetry line.

This means that one half of the figure is the mirror image of the other half. Imagine that you folded the figure along the symmetry line. Then both sides would exactly meet. Or, place a mirror along the symmetry line. You see the other half of the figure reflected in the mirror.

Some shapes you can fold two different waysso that the sides meet. The cross-shape on the right has two different symmetry lines.

Look at this flower shape. It has four different symmetry lines.

Check them by using the mirror.

Any line that you draw through the circle'scenter point is a symmetry line.

So, we can't even count how many symmetry lines a circle has! Draw you one more examplein the last circle.

Some shapes have only one symmetry line, like this arrow shape.

Many figures are not symmetrical at all.

a. b. c. d. e.


http://www.MathMammoth.com

2. Is the line drawn a symmetry line for the figure?

3. Draw different symmetry lines to these figures.

4. Write the capital letters to which you can draw a symmetry line. Draw the symmetry lines to them.

The case of the parallelogram

Does a parallelogram have a symmetry line like this? Use a mirror to check! Or, draw a parallelogram, cut it out, and fold it along the diagonal line. Do the two folded sides match?

Here's the answer: The red dotted line shows you how the folding would go. The two sides don't match, so the blue dashed line is NOT a symmetry line.

a. b. c. d. e. f.

g. h. i. j. k. l.

a. b. c. d.

e. f. g. h.


http://www.MathMammoth.com

Perimeter

1. Find the perimeter.

2. Find the perimeter....

a) of a square with sides 15 inches in length.

b) of a rectangle with 7 cm and 18 cm sides.

3. If the perimeter of a square is 64 cm, what is the length of the sides?

Perimeter is an extremely easy concept; the trouble comes in remembering the word and what it means.

Think of it this way: peri-meter means the "walk-around-measure", the distance you cover if you walk all the way around the figure.

The word comes from Greek word perimetros, and in it peri means "around" and metros means "measure".

What is the perimeter?

To find the perimeter, just add all the side lengths together.

Often you need to figure out some side lengths that are not given.

What side lengths are not given? What is the perimeter?

a. 6

b. c.

d. e.

f.


Chapter 8: Measuring Introduction

The eighth chapter of Math Mammoth Grade 3-B Complete Worktext covers measuring-related topics. Both metric system and customary system units are covered. The lessons still contain plenty of hands-on exercises, but the emphasis is shifting to the abstract conversions between different measuring units. The later grades will practice the unit conversion even more, of course.

The student will first learn to measure short distances to the nearest quarter inch, and using centimeters and millimeters. Then, the lessons cover units used for longer distances: First, the customary system of units feet, yards, and miles, and then the metric system of ones meters and kilometers.

Next, comes measuring weight. The student learns how to measure the weight of light objects using ounces and then grams. The lessons also practice the conversion between units.

After that we study measuring volume. Here the student is expected to know the units cup, pint, quart, and gallon from the second grade. The lesson practices them further, and introduces fluid ounces. Then comes a lesson about the metric system units for volume: milliliters and liters.

The last two lessons deal with measuring temperature, using Fahrenheit or Celsius scale.

We all use various measuring units in our everyday life, and using them is the key to remembering what they are and what the conversion factors are. Naturally, people in the United States often do not use the metric system a lot, while people elsewhere do not use the customary system. The units your child is not using are likely to be forgotten easily. So encourage the student(s) to have free play time with measuring devices such as a scale, measuring cups, a measuring tape, and rulers.

The Lessons

Helpful Resources on the Internet

page spanMeasuring to the Nearest Fourth-Inch ............. 61 5 pagesCentimeters and Millimeters ............................ 66 4 pagesFeet, Yards and Miles....................................... 70 2 pagesMeasuring Length in the Metric System: Meters, Kilometers and More...........................

72

2 pages

Using Ounces ................................................... 74 5 pagesUsing Grams .................................................... 79 3 pagesPracticing with Units of Volume...................... 83 3 pagesMillileters and Liters ....................................... 86 2 pagesMeasuring Temperature: Fahrenheit................ 88 2 pagesMeasuring Temperature: Celsius..................... 90 2 pagesReview ............................................................ 92 2 pages

59

Measuring to the Nearest Fourth-Inch

If a line reaches till the 1/4-mark after the number 1, then the line is 1 inch and 1/4 inch long. But when writing and saying it, we omit the "and", and write: The line is 1 1/4 inches long.

If a line reaches till the 3/4-mark after number 2, then the line is 2 inches and 3/4 inch long, but we write it as 2 3/4 inches long.

This line is 3 1/2 inches long.

This ruler measures in inches. You can see three lines between each two numbers on the ruler. Those three lines divide each inch into four parts. The parts are fourth parts of an inch. We have marked those fourth-parts with fractions.

The 2/4 mark is also the 1/2 mark. We normally use 1/2 instead of 2/4.

This line is 1/4 inch long.

This line is 2/4 inch long. It is also 1/2 inch long.

This line is 3/4 inch long.


5. Fill in the blanks, using the units "inches", "feet", "yards", and "miles".

a. Mark drove his car 15 _____________ in 15 minutes.

b. Annie's house is 32 ____________ long.

c. Karen's bedroom is 3 ___________ wide.

d. The snail traveled 5 ______________ in an hour.

e. The door was about 1 ____________ wide.

6. Use a tape measure to measure lengths of objects and distances in feet and inches.

7. Convert between feet and inches.

Remember 12 inches makes 1 foot.

Item How long

____ ft ____ in.

a. 1 ft = ____ in.

3 ft = ____ in.

5 ft = ____ in.

b. 1 ft 2 in. = ____ in.

1 ft 8 in. = ____ in.

1 ft 11 in. = ____ in.

c. 2 ft 4 in. = ____ in.

2 ft 6 in. = ____ in.

3 ft 3 in. = ____ in.

d. 12 in. = ____ ft

15 in. = ____ ft ____ in.

20 in. = ____ ft ____ in.

e. 24 in. = ____ ft

28 in. = ____ ft ____ in.

35 in. = ____ ft ____ in.

f. 36 in. = ____ ft

41 in. = ____ ft ____ in.

45 in. = ____ ft ____ in.


Practicing with Units of Volume

Volume means how much space something takes.

You are already familiar with cups, pints, quarts, and gallons. They are units of measure in the customary system.

Besides those, we use fluid ounces to measure small volumes. These are different from the ounces used to measure weight. Fluid ounces are abbreviated with "fl.oz." or just "oz" if there is no possibility for confusion with the other ounces.

Some units of volume in the customary system

8

2

2

4

ounce for small amounts of liquid (oz.)cup for small amounts of liquid (C)pint for medium-size amounts of liquid (pt)quart for medium-size amounts of liquid (qt)gallon for large amounts of liquid (gal)

2 cups makes a pint.

= =

2 pints makes a quart.

= 1 gallon

Four quarts makes 1 gallon.

In other words, 1 quart is one-fourth of a gallon. Indeed, the word "quart" is similar to a "quarter" or one-fourth.

1. Find 1-cup, 1/2-cup, and 1/4-cup measuring cups (used in baking). Then, find the markings on them that are for ounces.

a) Measure 1 ounce of water to a drinking glass.

b) Measure 2 ounces of water to a drinking glass.

c) Measure 4 ounces of water to a drinking glass.

d) Guess how many ounces of water would fit into the drinking glass. Then check.

e) Guess how many ounces of water would fit into a food container. Then check.

f) Fill in the blanks:

1 cup = ____ ounces

1/2 cup = ____ ounces

1/4 cup = _____ ounces

2 cups = ____ ounces

3 cups = ____ ounces


Chapter 9: Division Introduction

The ninth chapter of Math Mammoth Grade 3-B Complete Worktext covers the concept of division and basic division facts that are solved by knowing the multiplication tables.

The concept of division in itself is not very difficult. After all, it is like backwards multiplication. Children can have difficulties in related concepts, such as the remainder, divisibility, factoring, and long division. The aim of this chapter is to lay a good foundation in basic division, cementing the link between multiplication and division, and then solidly studying the concept of the remainder. Understanding these is required when later studying divisiblity, long division, and factoring.

The chapter provides plenty of practice and stresses understanding of concepts. I don't wish the student to memorize procedures without understanding the 'why' (rote memorization).

For example, when studying the remainder, the student first finds the remainder with the help of pictures -which is equivalent to using manipulatives. Then he explores the pattern found in dividing subsequent numbers by the same number, such as 25 ÷ 3, 26 ÷ 3, 27 ÷ 3, 28 ÷ 3, etc. After that, the method for finding the remainder is given as, "Look at the difference", and finally the typical school-book method with subtraction is presented.

The pre-requirement for studying division is knowing the times tables fairly well. You can still start here even if your child is still needing some practice with the tables, but she should finish mastering the tables fairly soon before you do a lot of division practice.

There are basically two ways of illustrating division with concrete objects. The first one can be explained by having some objects that you divide between a certain number of persons. For example, problem 12:3 can be asked, "If you have 12 bananas and 3 people, how many bananas does each one get?" The second one is in terms of grouping. The problem 12:3 would be: "If you have 12 people, how many groups of 3 people can you make?" These are important to understand so that your child can solve problems of everyday life where we use division. Therefore we need to do lots of word problems while studying division.

The Lessons page span

Division as Making Groups ................................ 96 4 pagesDivision and Multiplication ................................ 100 4 pagesDivision and Multiplication Facts ...................... 104 4 pagesDividing Evenly into Groups ............................. 108 4 pagesZero and One Division ...................................... 112 4 pagesWhen Division is not Exact ............................... 116 4 pagesChecking Division with a Remainder ................ 120 3 pagesFraction - Division Connection............................ 123 2 pagesReview of Division ............................................ 125 2 pages

94

Division as Making Groups

1. Divide into groups.

There are 12 daisies. Make groups of 3.

How many groups? How many 3's in 12?

a. There are ___ carrots. Make groups of 5.

How many groups? How many 5's in ____?

b. There are ___ berries. Make groups of 4.


c. There are ___ apples. Make groups of 3.


d. There are ___ fish. Make groups of 2.


e. There are ___ daisies. Make groups of 6.


f. There are ___ camels. Make groups of 4.



1. Make groups. Then write down the division and multiplication facts that the pictures are illustrating.

2. Now draw sticks or balls and make a picture yourself. Write the division and multiplication sentences.

a. Make groups of four.

___ × 4 = 8

8 ÷ 4 = ___

b. Make groups of two.

___ × 2 = ___

___ ÷ 2 = ___

c. Make groups of four.

___ × 4 = ___

___ ÷ 4 = ___

d. Make groups of six.

___ × 6 = ___

___ ÷ 6 = ___

e.

___ × 4 = ___

___ ÷ 4 = ___

f.

___ × 7 = ___

___ ÷ 7 = ___

g.

___ × 6 = ___

___ ÷ 6 = ___

h.

___ × 2 = ___

___ ÷ 2 = ___

i.

___ × 5 = ___

___ ÷ 5 = ___

a. Draw 15 sticks. Make groups of 5.

__ × 5 = __

__ ÷ 5 = __

b. Draw 24 sticks. Make groups of 8.

c. Draw 30 sticks. Make groups of 5.


2. Divide the dots so that groups have the same amount of dots and write a division sentence.

3. Divide and indicate the remainders. You can draw pictures! What patterns do you notice?

a. Divide evenly into 3 groups

20 ÷ 3 = ___, remainder ____

b. Divide evenlyinto 4 groups

21 ÷ 4 = ___,

remainder ___

c. Divide evenlyinto 6 groups

___ ÷ 6 = ___,

remainder ___

d. Divide evenlyinto 5 groups

___ ÷ 5 = ___,

remainder ___

e. Divide evenly into 7 groups

___ ÷ 7 = ___,

remainder ___

f. Divide evenlyinto 9 groups

___ ÷ 9 = ___,

remainder ___

g. Divide evenlyinto 3 groups

___ ÷ 3 = ___,

remainder ___

h. Divide evenlyinto 5 groups

___ ÷ 5 = ___,

remainder ___

a. b. c.

21 ÷ 2 = ___, R __ 22 ÷ 2 = ___, R __ 23 ÷ 2 = ___, R __ 24 ÷ 2 = ___, R __ 25 ÷ 2 = ___, R __ 26 ÷ 2 = ___, R __ 27 ÷ 2 = ___, R __ 28 ÷ 2 = ___, R __ 29 ÷ 2 = ___, R __ 30 ÷ 2 = ___, R __

21 ÷ 3 = ___, R __ 22 ÷ 3 = ___, R __ 23 ÷ 3 = ___, R __ 24 ÷ 3 = ___, R __ 25 ÷ 3 = ___, R __ 26 ÷ 3 = ___, R __ 27 ÷ 3 = ___, R __ 28 ÷ 3 = ___, R __ 29 ÷ 3 = ___, R __ 30 ÷ 3 = ___, R __

21 ÷ 4 = ___, R __ 22 ÷ 4 = ___, R __ 23 ÷ 4 = ___, R __ 24 ÷ 4 = ___, R __ 25 ÷ 4 = ___, R __ 26 ÷ 4 = ___, R __ 27 ÷ 4 = ___, R __ 28 ÷ 4 = ___, R __ 29 ÷ 4 = ___, R __ 30 ÷ 4 = ___, R __


Chapter 10: More on Multiplication Introduction

The tenth chapter of Math Mammoth Grade 2-B Complete Worktext deals with multiplying by whole tens, by 100, multiplying in parts, and using those skills to multiply vertically using an "easy way" - a variation of the standard algorithm.

The lesson Multiplying by Whole Tens and Hundreds does not give the rule for multiplying by whole tens or hundreds outright, but first asks the student to think based on examples. Multiplying a number by ten of course means just appending a zero to it: 10 × 24 = 240. If the student does not notice it, you can point it out. Similarly, if you multiply a number by 20, you can multiply it by 2 and append a zero, because multiplying by 20 is the same as multiplying by 2 and by 10. Continuing on, multiplying by 100 means appending two zeros to the number.

Later on in the lesson Multiplying in Parts. we study a very important principle that is normally called the distributive property. The lesson does not use that name but talks about "multiplying in parts". Basically, you multiply 6 × 17 by first multiplying 6 × 10, then 6 × 7, and adding the results. This principle is the basis for the procedure of multiplying vertically (in columns).

In the lesson Multiplying in Columns - the Easy Way we use this exact idea to multiply numbers in parts and adding the partial results. This way to multiply is just a variation of the common multiplication algorithm. Children will get plenty of practice of the more common way during fourth grade, but if you feel your child can grasp it, nothing prevents you from presenting it to your child now. The "easy way" just shows more plainly what the procedure is based on, and it is easier to understand why it works.

The Lessons

Helpful Resources on the Internet Rectangle Multiplication An interactive tool that illustrate multiplying in parts using the area model. Choose the "common" option for multiplying in parts. http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html

Math Playground Learn how to think algebraically with these clever weighing scales. http://www.mathplayground.com/algebraic_reasoning.html

page spanMultiplying by Whole Tens and Hundreds .............. 129 4 pagesUsing All Four Operations ....................................... 133 4 pagesMultiplying in Parts .................................................. 137 5 pagesMultiplying in Columns - the Easy Way ................. 142 3 pagesMultiplying in Columns - the Easy Way, Part 2 ...... 145 2 pagesReview ...................................................................... 147 1 page

127

http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html

http://www.mathplayground.com/algebraic_reasoning.html

8. Write a mathematical sentence or each word problem. You will need to use all four operations!

a. Each of the three sacks contains four small bags. Each small bag has eight marbles. How many marbles total are in all the sacks? (Draw a picture!)

b. The school has 120 pupils in the upper grades. On lower grades are nine classes with 12 pupils in each. How many pupils are in the school?

c. Amy's cat has had seven litters in her life. Six of those litters had five kittens and one had seven. How many kittens has Amy's cat had?

d. A construction block set had 150 pieces, but 14 have broken. Then Jack got another set of 70 blocks. How many blocks does he have now?

e. The music school has 90 students divided evenly into nine classes. Then the class that Jill was in got two new students. How many students are now in Jill's class?

f. Each of the 10 classrooms in the school has four windows, except one only has 3. How many windows are there total?

g. 58 kids in kindergarten are put into classes with 10 kids in each class. How many classes will there be?

h. The teacher bought six packages with eight crayons and five packages with ten crayons. How many crayons did she buy?

i. Chloe has 28 marbles, and Jenny has 52. They combined the marbles and then shared them equally. How many marbles did each girl get?

j. Jerry bought 40 horse shoes for his eight horses. How many shoes will not be used?

k. Can a teacher divide 98 colored pencils equally between her 20 students? How would you do the division?

l. Should the gardener arrange his 48 plants eight in a row, or nine in a row?


Chapter 11: Fractions Introduction

The 11th and last chapter of Math Mammoth Grade 3-B deals with a few elementary fraction concepts: fractions, a part of a whole, mixed numbers, and adding and subtracting like fractions.

First, the student learns to name fractions and to draw "pie models" for the most common fractions. The CD contains cutout pie models for common fractions that you can print out and use to illustrate fractions. They are especially useful when studying fraction addition and subtraction in this chapter.

The lesson Part of a Whole Group is very important, and this concept has been touched on previously as well (see the lesson Fraction/Division Connection in chapter 9).

The lesson about mixed numbers only contains picture exercises, along with some number lines. I feel strongly about letting children do fraction operations with pictures or manipulatives until they thoroughly understand the concept, and not introducing the various fraction calculation rules too soon. That is why this lesson does not mention the rule that "to change a mixed number to a fraction, multiply the whole number part by the denominator, and add the numerator."

For the same reason, the next lesson on adding and subtracting fractions also does not spell out the "rule" for adding and subtracting like fractions. The student works with pictures and writes addition and subtraction sentences, thus building his understanding of the process. We can leave the various rules for 5th grade.

This chapter also contains a very introductory lesson on decimal numbers with one decimal digit - or those with tenths.

The Lessons

Helpful Resources on the Internet Visualizing Fractions The other way around as in the previous activity: the computer shows a fraction, and you divide the pie and color the pieces. http://nlvm.usu.edu/en/nav/frames_asid_103_g_2_t_1.html

page spanUnderstanding Fractions ................................. 150 3 pagesPart of a Whole Group .................................... 153 3 pagesMixed Numbers .............................................. 156 4 pagesAdd and Subtract Like Fractions .................... 160 3 pagesDecimal Numbers - Tenths ............................. 163 2 pagesFractions Review ............................................ 165 1 page

148

http://nlvm.usu.edu/en/nav/frames_asid_192_g_2_t_1.html

http://www.mathplayground.com/algebraic_reasoning.html

Understanding Fractions Fractions are PARTS of a WHOLE. The WHOLE is always divided into EQUAL parts.

1. Color parts to illustrate the fraction.

One part is colored; two equal parts; one half.

1 2

Two parts are colored; two equal parts; two halves OR one whole.

2 2

= 1

One part is colored; four equal parts; one fourth.

1 4

Two parts are colored; five equal parts, two fifths.

2 5

Three colored parts; seven equal parts; three sevenths.

3 7

Can you tell what fraction this is?

"three eighths"

3 8

NUMERATOR DENOMINATOR

The number ABOVE the line tells HOW MANY PARTS are colored. It enumerates or counts the colored parts.

The number BELOW the line tells WHAT KIND OF PARTS the whole is divided into. It denominates or names the parts.

We use ordinal numbers to name the fractional parts.

a. b. c. d. e. f.

7 8

6 10

4 6

4 5

2 4

4 7

g. h. i. j. k. l.

2 6

11 12

5 9

1 5

9 10

2 7


2. Write the fractions, and read them aloud.

3. Draw the pie models and color the parts to illustrate the fractions.

a. b. c. d.

e. f. g. h.

i. j. k. l.

How to draw pie models

Halves: split the circle with a straight line.

Thirds: draw lines at 12 o'clock, 4 o'clock, and 8 o'clock.

Fourths: First draw halves, then split those like a cross pattern.

Fifths: Draw as a man doing jumping jacks.

Sixths: First draw thirds, then split those

Eighths: First draw fourths, then split those.

a.2 3

b.

2 5

c.

1 6

d. 6 8

e.4 5

f.3 8

g.1 3

h. 4 4


4. Draw the fractions. Then compare: which is more pie? Write > , < , or = between the fractions.

What can you notice about comparing two fractions when the denominators are the same?

What can you notice about comparing two fractions when the numerators are the same?

a.

2 3

1 3

b.

1 5

4 5

c.

1 6

3 6

d.

6 8

7 8

e.

3 8

1 8

f.

2 4

4 4

g.

1 9

5 9

h.

5 12

3 12

i.

6 10

7 10

j.

1 2

1 3

k.

1 5

1 8

l.

1 6

1 2

m.

1 6

1 8

n.

1 2

2 3

o.

4 8

4 5

p.

2 4

2 6

q.

3 8

3 6

r.

1 2

2 4


math mammoth grade 3-b complete worktext samples · chapter 6: place value with thousands...

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