Contents. Chapter 6: Geometry and Fractions

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2 Contents Chapter 6: Geometry and Fractions Introduction... 5 Shapes Review... 7 Right Angles... 9 Parallel and Perpendicular Lines... Forming Shapes... 5 Solids... 6 Fractions... 7 More on Fractions... 9 Chapter 7: Place Value Till 000 Introduction Hundreds Part Hundreds Part Skip-Counting Practice... 3 Seven Hundred to Thousand Counting and Adding Which Number is Greater? Comparing and Ordering Chapter 8: Mental Addition and Subtraction Introduction Completing the Next Hundred Add and Subtract Whole Hundreds... 5 Practice with Whole Hundreds Addition/Subtraction Connection Graphs Adding Whole Tens... 6 Subtracting Whole Tens Adding Ones Subtracting Ones Mentally Review of Mental Math

3 Chapter 9: Measuring Introduction Exploring Measuring Inches and Half-Inches Measuring to the Nearest Centimeter Measuring to the Nearest Half-Inch Feet and Miles Metric System: Meters and Kilometers Weight in Pounds Weight in Kilograms Estimate Weight Volume Volume in Milliliters Review Chapter 0: Adding and Subtracting in Columns Introduction Adding 3-Digit Numbers in Columns Carrying to Hundreds Carrying to Tens and to Hundreds Subtracting in Columns... 0 Borrowing Two Times... 4 Adding Money Amounts... 7 Review... 9 Chapter : Exploring Multiplication Introduction... 2 Many Times the Same Group Multiplication and Addition Multiplying on a Number Line Multiplication Practice Review

4 Chapter 6: Geometry and Fractions Introduction The sixth chapter of Math Mammoth Grade 2-B Complete Worktext covers geometry topics and an introduction to fractions. In geometry, the emphasis is still on exploring shapes: Combining shapes to get new ones, and dividing shapes with lines to get other shapes. The student also learns the concepts of right angle and parallel lines. These two concepts get the child started on the road to classifying shapes by their angles and sides. For example, later the child will classify triangles into right triangles, acute triangles, and obtuse triangles. Quadrilaterals are classified into rectangles, parallelograms, kites, trapezoids, and so on. Finding a right angle or parallel sides in a shape is therefore important. Introduction to fractions In the section on fractions, the student learns to write fractions from pictures or color parts to show a fraction. The student should also learn that when comparing unit fractions, the one with the largest denominator is actually the smallest part. The child does not need to know this language yet, of course. The basic idea is simple: One-half is a bigger part than one-fifth. The last lesson explores finding a fractional part of many objects. It is important that children do not "fixate" the idea of a fraction to just pies or other shapes divided into parts. They need to also understand that fractions can be used when the "whole" is a group of things. The Lessons page span Shapes Review pages Right Angles pages Parallel and Perpendicular Lines... 2 pages Forming Shapes pages Solids... 6 page Fractions pages More on Fractions pages 5

5 Right Angles These look like corners, but in mathematics we call them angles. Imagine sitting inside each angle, and the walls going up around you in the shape of the "corner". In which angle would you have lots of space to sit? In which angle would you have only a little space to sit? Find two "straight corners". In math we call them right angles. Sometimes we draw a round line (an arc) inside the angle to mark it. Right angles are marked this way. Corners of books are examples of right angles.. Write how many angles each shape has. Write how many right angles each shape has. a. angles right angles b. c. angles angles right angles right angles d. e. f. angles angles angles right angles right angles right angles 9

6 Solids A rectangular prism In everyday speech we call it a "box". A cube is a box, too, but all of its sides are equally long. A cylinder has the same-size circle on the bottom and at the top. A pyramid's bottom shape can be any many-sided figure. A cone has a circle at one end and a point at the other.. Label the pictures with box, cube, cylinder, pyramid, or cone. a. b. c. d. e. f. g. h. i. j. k. l. m. n. o. p. 6

7 More on Fractions. In each picture, color one part of the whole, and write the fraction. Circle the largest fraction. a. b. c. d. 2. Color the fractions in the fraction bars on the left. 5 0 Find the smallest fraction. Find the greatest fraction Color the fractions in the fraction bars on the right. 6 Find the smallest fraction. Find the greatest fraction. Write a fraction that is smaller than any of these: Color one part of each. Circle the fraction that is more: a. 3 or 2 b. 2 or 5 c. 5 or 4 d. 5 or 6 e. 8 or 6 f. 2 or 8 8

8 Chapter 7: Place Value Till 000 Introduction The seventh chapter of Math Mammoth Grade 2-B Complete Worktext deals with three-digit place value - ones, tens, and hundreds. The first lessons present three-digit numbers with hundred-flats, ten-pillars, and one-cubes. The child practices separating three-digit numbers to the different "parts": hundreds, tens, and ones. Number lines will help visualize the numbers and build number sense. These lessons provide the basis for understanding three-digit place value. The lesson Skip-Counting Practice shows how to add or subtract a ten: you look at the tens digit in the number, and add or subtract from it. In counting practice, emphasize the similarity to numbers that are less than 00. For example, in counting by fives from 305, the sequence is essentially the same as if counting by fives from 5, but just with the "three hundred" added each time. The Counting and Adding lesson has further practice. The student forms three-digit numbers from their parts, compares, fills number charts, and adds. The lesson, Which Number is Greater, has very simple exercises about comparing numbers. Then, the Comparing and Ordering lesson has further practice, plus some more advanced exercises. For example, the student compares sums, and finds a number on the empty line so that the comparison sentence is true. This last lesson also has a fun domino game where students build three-digit numbers and try to get them as close as possible to a given whole hundred. The Lessons page span Hundreds Part pages Hundreds Part pages Skip Counting pages Seven Hundred to pages Counting and Adding pages Which Number Is Greater? pages Comparing and Ordering pages 22

9 Hundreds, Part Ten ones make a ten-pillar: Ten ten-pillars make ONE HUNDRED: = = 0 ones = 0 0 tens = 00 Just like tens and ones, so also whole hundreds are counted separately and are written down in their own column: = hundreds tens ones three hundred twenty-seven. Count the ones, tens, and hundreds and fill in the table. a. One hundred one b. One hundred six c. One hundred eleven d. One hundred thirteen hundred 0 tens one hundred 0 tens 6 ones hundred ten one hundred tens 3 ones hundreds tens ones 0 hundreds tens ones hundreds tens ones hundreds tens ones 24

10 . What are these broken down numbers? Counting and Adding a = = d = = g = = b = = e = = h = = c = = f = = i = = 2. Underline what is more. Write as numbers too. a. 6 hundreds hundreds 500 b. 2 hundreds 4 tens 4 hundreds c. 7 hundreds 7 hundreds 9 ones d. 3 hundreds 9 ones 3 hundreds e. 3 hundreds 9 hundreds 3 tens f. 8 hundreds 7 hundreds 9 ones g. hundred 6 tens 3 hundreds h. 3 hundreds 5 tens 4 hundreds 8 tens i. 2 hundreds 2 tens 2 hundreds j. 3 hundreds 8 ones 8 hundreds 3 ones k. 2 hundreds 7 ones 2 hundreds 5 tens l. 5 hundreds 5 tens 5 hundreds ten 36

11 Comparing and Ordering. Mark the numbers on the number line. Then write them in order. 80, 725, 799, 802, 843, 795, 80, 80, 866, 829 < < < < < < < < < 2. Write either < or > in between the numbers. a. 50 < 55 b c d e f g h i j k l m n o p q r s t

12 Chapter 8: Mental Addition and Subtraction Introduction The eighth chapter of Math Mammoth Grade 2-B Complete Worktext covers mental adding and subtracting topics with 3-digit numbers. The goal of this whole chapter is to solidify children's understanding of 3-digit place value, since being able to subtract to add and subtract whole hundreds, whole tens, and ones is based on understanding well the 3-digit place value. These problems build number sense and also build children's understanding of addition and subtraction. In most lessons, the addition or subtraction is first illustrated with pictures so the student can learn the concepts relating to the different place values. You can obviously also use base ten blocks or other similar manipulatives to this end. The lesson on graphs uses three-digit numbers in contexts of problems. The Lessons page span Completing the Next Hundred pages Add and Subtract Whole Hundreds pages Practice with Whole Hundreds pages Addition/Subtraction Connection pages Graphs pages Adding Whole Tens pages Subtracting Whole Tens pages Adding Ones pages Subtracting Ones Mentally pages Review of Mental Math page Helpful Resources on the Internet Use these free online resources to supplement the "bookwork" as you see fit. Random Stop 000 Place digits strategically into the addition problem so that the sum is as close as 000 as possible. 47

13 Completing the Next Hundred + = 60 + = 00 + = = 300 We need 0 ten-pillars to make a hundred. Draw the missing ones.. Compare and complete the next hundred. a = = = b = = = c = = = 2. Complete the next hundred and write a corresponding problem where you complete just 00. a = = 00 d = + = 00 b = = 00 e = + = 00 c = = 00 f = + = Complete the next hundred. a = 600 b = 600 c. 0 + = d = e = f = g = h = i = 000 j = k = l = 47

14 2. Cross out as many hundreds as the problem indicates. Do the problems in columns as well. H T O H T O a = b = H T O H T O c = d. 200 = H T O H T O e. 00 = f. 200 = H T O H T O g. 500 = h. 400 = Only the digit changes in the answer. 52

15 Adding Whole Tens. Add whole tens. and a = and b = and and c. + = d. + = Now draw the pictures. e = f = g = h = With these problems, the hundreds' digit and the ones' digit do not change in the answer. (Later you will see problems where the hundreds digit will change.) 2. Count by tens - up and down! a. 700, 70,,,,,,,,,, b.,,,,,, 270, 280,,,, c.,,,, 390, 380,,,,,, 6

16 Chapter 9: Measuring Introduction The ninth chapter of Math Mammoth Grade 2-B Complete Worktext covers measuring length, weight, and volume. The lesson "Exploring Measuring", conveys the idea of measuring as repeatedly applying the measuring unit. In the rest of the lessons, the student learns many of the commonly used measuring units. The student measures length in inches and half-inches, and learns to measure to the nearest half-inch or to the nearest centimeter. The bigger units feet, miles, meters, and kilometers are also introduced but this grade does not yet include conversions between the units. The lessons on measuring weight have several activities to do at home using a bathroom scales. The goal is to let students become familiar with pounds and kilograms, and have an idea of how many pounds or kilograms some common things weigh. In order to estimate weight, a child has to know the approximate weights of some objects, and then compare the weight of the unknown object to some known weight. This knowledge is gained through experience. Similarly, in studying volume, the lessons include many hands-on activities so that the student gets firsthand experience in measuring, and has a basic knowledge of how "big" the units cup, pint, quart, gallon, milliliter, and liter are. When it comes to measuring, experience is the best teacher. So, encourage your child to use measuring devices (such as a measuring tape, scales, and measuring cups), and to "play" with them. In this way the various measuring units start to become a normal part of his life, and are never forgotten. In third grade, the study of measuring turns towards conversions between the different units. So these activities are laying an important foundation on the concrete level. The Lessons page span Exploring Measuring page Inches and Half-Inches pages Measuring to the Nearest Centimeter pages Measuring to the Nearest Inch pages Feet and Miles pages Metric System: Meters and Kilometers page Weight in Pounds pages Weight in Kilograms pages Estimate Weight page Volume pages Volume in Milliliters pages Review page 74

17 Exploring Measuring We measure things to find how much a thing weighs as compared to other things how long or wide a thing is as compared to other things how much space a thing takes as compared to other things how much liquid a thing holds as compared to other things.... and much much more. For all measuring, you need a measuring unit. You repeat the measuring unit many times, and compare to the thing you are measuring.. Measure how wide a table is, using a small shoe and then a big shoe as a measuring unit. It is enough to have the left and the right shoe. Place the left shoe at the edge of the table, and the right shoe right after the left. Then move the left shoe in front of the right, and so on. Keep count. The table is small shoes wide. The table is big shoes wide. 2. Fill a small pot or bucket with water. Measure the amount of water using a coffee cup, or a pint jar. The pot holds coffee cups of water. The pot holds pint jars of water. 3. Billy measured how wide his book was. First he used paperclips, and then small crayons. His book was 0 paperclips wide. How many small crayons wide was the book? 4. Why don't people use Daddy size shoes or paperclips as measuring units? Look carefully at Billy's paperclips and crayons. 5. Ryan measured that his room was 27 Daddy-size shoes wide. He also measured it using baby shoes. Ryan's room was 80 / 0 baby shoes wide (circle the right number). 75

18 Feet and Miles This is a tape measure. The numbers, 2, 3, and so on, are inches. Number 2 is on a black background, and above it you see "F". That means foot. 2 inches makes foot. Roll the tape measure out some more, until you find "2 F" or "2 ft" (which means two feet), and "3 ft" (three feet), and so on. Stretch out the tape measure as far as you can. What is the biggest number of feet it has? You use feet as your measuring unit when you measure the width of a room or of a table, the length of a house, or of a swimming pool. People often use both feet and inches. For example, a table can be 5 feet 0 inches long. A boy can be 4 feet 7 inches tall. This tape measure has both inches and centimeters. The numbers in the top part are inches, and the numbers in the bottom part are centimeters. The number 60 means 60 cm, and the "" after it means 6 cm. Measuring tapes often have centimeters on one side and inches on the other side. Distances between towns or between countries are measured in miles. mile is 5,280 feet (five-thousand two-hundred eighty)! That is a lot of feet - many, many more than your tape measure has.. Find a pair of big shoes such that each shoe is foot long (2 inches), or use two -foot long rulers. Using the shoes or rulers, measure how many feet wide is: a) the room you are in feet b) a table feet c) feet 82

19 Chapter 0: Adding and Subtracting in Columns Introduction The tenth chapter of Math Mammoth Grade 2-B Complete Worktext deals with addition and subtraction in columns using three-digit numbers. In the first lesson, the student adds three-digit numbers, carrying to tens when it is necessary. The next lesson is about the situation when there are more than ten tens, so carrying to hundreds is necessary. This is first illustrated with pictures, and then practice problems follow. In the third lesson, the student carries two times - both to tens and to hundreds. The pictures in the beginning of the lesson show ten ones grouped to form a new ten, and ten tens grouped to form a new hundred. Please spend some time studying with these pictures. There are two processes happening in the same situation. Next comes subtracting in columns. In the first lesson, Subtracting in Columns, the student borrows one time per problem - either from the tens or from the hundreds. The pictures show how a ten is broken into ten ones or how a hundred is broken into ten tens. The concept of borrowing two times can be a bit tricky. This is studied more in third grade. Lastly, the chapter includes a lesson in adding money amounts, which is probably easy after the previous addition practice. The Lessons page span Adding 3-Digit Numbers in Columns pages Carrying to Hundreds pages Carrying to Tens and to Hundreds pages Subtracting in Columns... 4 pages Borrowing Two Times pages Adding Money Amounts pages Review pages 98

20 Carrying to Tens and to Hundreds 0 little ones form a new ten. 0 tens form a new hundred. Total is Can you see that in the picture? hundreds tens ones Add in ones column: = 4. There are more than ten ones, so carry to tens column. Add in tens column: = 2. There are more than ten tens, so carry to hundreds column. 0 little ones form a new ten. 0 tens form a new hundred. Total is Can you see that in the picture? hundreds tens ones Add in ones column: = 4. There are more than ten ones, so carry to tens column. Add in tens column: = 0. There are more than ten tens, so carry to hundreds column. You have to carry to the tens and to the hundreds. You have to carry two times. 06

21 4. Add. Carry two times if necessary. a b c d e Solve the word problems. Write number sentence(s) for each. You can add or subtract in columns. a) From Flowertown to Princetown is 42 miles. How many miles is a round trip Flowertown-Princetown-Flowertown? b) The school bought pencils for $28, pens for $29, and notebooks for $549. Find the total bill. c) One side of a rectangle is 56 feet and another side is 277 feet. Draw a picture and mark the side lengths. d) If a car goes 50 miles with gallon of gasoline, how far will it go with 2 gallons of gasoline? How about with 3 gallons? With 4 gallons? How long a distance do you walk if you walk all around it? How many gallons will it take to travel 400 miles? What numbers are missing from the additions?

22 Chapter : Exploring Multiplication Introduction The th and last chapter of Math Mammoth Grade 2-B covers the multiplication concept, its connection with repeated addition and some easy multiplication practice. The lessons here are self-explanatory. The student first learns the meaning of multiplication as "many times the same size group". Then there is practice writing multiplications as repeated additions and vice versa. Number line jumps are another way to illustrate multiplication. The actual study and memorization of the multiplication tables is in the third grade. However, you can certainly help your child to notice the patterns in the easy tables of 2, 5, and 0, and encourage their memorization. If the time allows and the child is receptive, you can study multiplication tables even further at this time. The Lessons page span Many Times the Same Group pages Multiplication and Addition pages Multiplying on a Number Line pages Multiplication Practice pages Review pages Helpful Resources on the Internet Use these free online resources to supplement the "bookwork" as you see fit. Math Dice Game for Addition and Multiplication Instructions for three simple games with dice; one to learn multiplication concept, another to practice the times tables, and one more for addition facts. Explore the Multiplication Table This applet visualizes multiplication as a rectangle. Multiple Counting Practice Click on the numbers on the grid to skip count. 22

23 3. Fill in the missing parts. a. 2 times 5 b. times c. times d. times e. times f. times 5 3 This means "5 times a group of 3". It is multiplication. 2 7 This means "2 times a group of 7". You multiply 2 times Your turn to draw! Notice also the symbol which is read "times". a. 2 times b. 3 times c. times 7 7 d. 6 times 6 e. 4 times f. 2 times

24 Multiplying on a Number Line Five jumps, each is two steps. 5 2 = 0. Four jumps, each is three steps. 4 3 = 2.. Write the multiplication sentence that the jumps on number line illustrate. ` a. b. c. d. 30