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2 Contents Foreword... 5 Chapter 1: Addition Within 010 Introduction... 6 Two Groups and a Total Learn Symbols + and = Addition Practice Which is More? Missing Items Sums with Sums with Adding on a Number Line Sums with Sums with Addition Practice Sums with Sums with Some Symbols Review of Addition Facts Chapter 2: Subtraction Within 010 Introduction Subtraction is 'Taking Away' Count Down to Subtract Subtraction and Addition in the Same Picture When Can You Subtract? Subtraction and Addition Two Parts One Total Fact Families How Many More? Difference or How Many More? Missing Addend Problems and Fact Families Review
3 Chapter 3: Addition and Subtraction Facts Introduction Addition and Subtraction Facts with 4 and Addition and Subtraction Facts with Addition and Subtraction Facts with Addition and Subtraction Facts with Addition and Subtraction Facts with Addition and Subtraction Facts with Adding and Subtracting Many Numbers Review Facts with 6, 7, and Review Facts with 9 and
4 Foreword Math Mammoth Grade 1A and Grade 1B worktexts comprise a complete math curriculum for the first grade mathematics studies. The main topics during first grade are the concepts of addition and subtraction, addition and subtraction facts, and place value till 100. Other topics studied are clock to the half hour, measuring length in inches and centimeters, shapes, and coins. When you use these books as your only or main mathematics curriculum, they can be like a "framework", but you still have a lot of liberty in planning your child's studies. While addition and subtraction topics are best studied in the order they are presented, feel free to go through the geometry, clock, and money sections in some different order. This might even be advisable if your child is "stuck" on some concept, or is getting bored. Sometimes the brain "chews the cud" in the background, and the concept she was stuck on can become clear after a break. This curriculum aims to concentrate on a few major topics at a time, and study them in depth. This is thus totally opposite to the continually spiraling stepbystep curricula, in which each lesson typically is about a different topic from the previous or next lesson, and includes a lot of review problems from past topics. This does not mean that your child wouldn't need occasional review. However, when each major topic is presented in its own chapter, this gives you more freedom to plan the course of study and choose the review times yourself. In fact, I totally encourage you to plan your mathematics school year as a set of certain topics, instead of a certain book or certain pages from a book. For review, I have included an html page called Make_extra_worksheets_grade1.htm that you can use to make additional worksheets for computation or for number charts. You can also always simply reprint some already studied pages. Also, the third chapter that practices addition and subtraction facts contains a lot of pages with problems, so you can choose to "save" some of them for later review. I wish you success in your math teaching! Maria Miller, the author 5
5 Chapter 1: Addition Within 010 Introduction The first chapter of Math Mammoth Grade 1A Complete Worktext covers addition concept and addition facts within The chapter starts out with very easy addition problems within 05, using pictures. If your child does not yet know the symbols + and =, you can introduce them first orally. In other words, use blocks or rocks and make addition problems where you use both kinds of wordings: "Three blocks and four blocks makes seven blocks. Three blocks PLUS four blocks EQUALS seven blocks." Play like that till the child can use the words PLUS and EQUALS in her own speech. This will make it easier for her to use the written symbols. Soon the lessons start including 'missing addend' problems. We first use pictures, and gradually get to the abstract 1 + = 5 with symbols only. Keep in mind that children may confuse this problem with =. You can word these problems like this: "1 and how many more makes 5?" You can MODEL them by drawing: First draw 1 ball. Tell the child that we need to have 5 balls in total. He is to draw more until there are five balls. In the missing addition problem, however many balls the child has to draw is the number that goes on the empty line. So, first there is one ball, then we need to add (draw) some more to make 5. But how many more were drawn? After that, the chapter contains many lessons called Sums with... whose goal is to help the child memorize addition facts. My approach to memorization is manyfold: 1. Structured drill, such as you see in the lessons Sums with 5, Sums with 6, and so on. This is not random drill, because you will start it by showing the pattern or the structure in the facts. This will help the student to tie the addition facts in with a context and help him understand the facts more on a conceptual level, instead of merely memorizing them at random. In sums with 5, the child learns the number combinations that add up to 5: 0 & 5, 1 & 4, and 2 & 3. This understanding is the basis for the drills. 2. Using addition facts in games, in math problems, everyday life, or anywhere else. Games are especially useful because they help children like mathematics. 3. Random drilling may also be used as a tool among others. 4. Memory helps such as silly mnemonics or writing math facts on a poster and hanging it on the wall. These are not needful for all kids. However, keep in mind that children will need LOTS of opportunities to add numbers to actually memorize the facts, so the memorization may not totally occur as your child works through this chapter. These same addition facts are further studied and used in the next chapters about subtraction, and in all later math work since they are constantly used. At the latest, your child should memorize addition facts during second grade, as recommended by the National Council of Teachers of Mathematics (NCTM). Please see the following page for a few games that I recommend using while studying this chapter. 6
6 1. Separate the balls into two groups. Two Groups and a Total and and and and 2 2 and 3 1 and 4 2. Separate the balls into two groups. Write how many are in the second group. a. 4 b. 4 c. 4 1 and d. 5 2 and e. 5 3 and f. 5 4 and g.5 3 and h. 5 2 and i. 5 1 and 2 and 0 and 10
7 Learn Symbols + and = = 5 THREE plus TWO equals FIVE = ONE plus THREE equals FOUR 1. Add. Read the addition sentences aloud using 'plus' and 'equals'. a. b. c = = + = d. e. f. + = + = + = g. h. i. + = + = + = j. k. l. + = + = + = m. + = n. + = o. + = 13
8 1. Draw more in the second group, and add. Addition Practice = = = = = = = = = 2. Draw dots. Add = = = = = = 15
9 Missing Items Something is missing from the addition. The TOTAL is not missing. We know the total. How many are in the second group? That's what is missing! Read: "2 plus what number makes 4?" "2 and how many more makes 4?" 1 + = 5 There should be 5 dots in all. Draw 4 in the second die face makes = 4 1. Draw more dots. 1 + = = = = = = = = = 4 19
10 Sums with 6 1. Six hippos are grouped into two groups, in different ways. Write the addition sentences. 2.Add = = = = = = = = = = = = = = = = 3. Drill. Don't write the answers but just think in your head. 1 + = = = = = = = = = = = = 6 24
11 Adding on a Number Line = 8 First jump 5... Then jump 3 more. You land at Draw jumps to illustrate the addition and find the answer. You can use two different colors to draw the jumps. a = b = c = d = e = f = 26
12 Sums with 9 1. Nine balls are grouped into two groups, in different ways. Write the addition sentences. 2. Add = = = = = = = = = = 3. Drill. Don't write the answers here. Just think in your head. + 8 = = = = = = = = = = = = = = = 9 39
13 Some Symbols 7 = 7 Seven equals seven. 6 = Six equals two plus four. = means "EQUAL". 7 8 Seven is not equal to eight Three plus four is not equal to five. means "NOT EQUAL". 1. Equal or not? Write = or. Read the sentences aloud Pick a number for the blank line so the comparison is true < 6 < 5 > 6 > > 7 < 5 > 6 < 3 47
14 Chapter 2: Subtraction Within 010 Introduction The second chapter of Math Mammoth Grade 1A Complete Worktext covers subtraction concept, its various meanings, and addition/subtraction connection. Subtraction concept If your child does not yet know the minus symbol " ", it is a good idea to introduce it first orally, without any pencil and paper work. Simply take blocks, rocks, or matches. Show the child eight blocks, and take away three blocks. Then use both kinds of wordings: "Eight blocks takeaway three blocks leaves five blocks. Eight blocks minus three blocks equals five blocks." Play with the blocks or other concrete things till the child can use the words MINUS and EQUALS in his/her own speech. This will make it much easier to then introduce the actual written symbols. In the first lessons, the child can figure out the subtraction problems by simply counting how many objects are left. Subtraction vs. addition How does one learn how to subtract without using concrete objects or pictures? How can the child subtract when she sees only numbers and there are no objects nor pictures to count? As a transitional strategy, you can teach the child to count down: to solve 95 for example, the child counts down five steps from nine: eight, seven, six, five, four. So four is the answer. But the final goal is to learn use the addition facts to find the answer to subtraction  in essence to memorize the basic subtraction facts, which are based on the addition facts. For this purpose, one has to of course learn the connection between addition and subtraction very well, and several lessons in the chapter help your the child to do just that. Other meanings of subtraction Besides 'taking away', subtraction is also used for these situations: Finding how much MORE something is as compared to something else. Note that no one "takes away" anything in this situation. It is about the difference. Two (or more) parts make up a whole (of something). If you know the whole and one part, find out the other part. This is approached in this ebook as being a missing addend problem. For example if the whole is 10 and one part is 7, we know the parts add up to 10. So you can write 7 + = 10. This itself CAN be solved by subtraction, or simply by one's knowledge of addition facts. These two situations are taught explicitly and can be found in the word problems throughout the book. 54
15 Subtraction is 'Taking Away' From five bananas we take away three. There are two left. 5 3 = 2 Five minus three equals two From six carrots we take away one. There are five left. 6 1 = 5 Six minus one equals five 1. Cross out some. How many are left? Read each subtraction sentence aloud using the words 'minus' and 'equals'. 10 total. Cross out 4. How many are left? 6 total. Cross out 6. How many are left? 8 total. Cross out 2. How many are left? a = b. 6 6 = c. 8 2 = 8 total, cross out 7. 8 total, cross out 6. 7 total, cross out 3. d. 8 7 = e. 8 6 = f. 7 3 = 57
16 Subtraction and Addition in the Same Picture Add: How many colored balls? How many white ones? Add: + = 10 + = 7 Subtract: Cover the colored balls. Write a subtraction sentence. Subtract: Cover the colored balls. 10 = 7 = 1. Make an addition sentence and a subtraction sentence from the same picture. + = 7 = + = 6 = + = 5 = + = 6 = + = 8 = + = 6 = 64
17 Fact Families Two addition facts and two subtraction facts form a fact family if they use the same three numbers. For example, with 5, 3, and 2 we get a fact family: = = = = 3 1. Write the fact families to match the pictures. / 6 / 8 a = = 6 6 = 6 = b. / / c. d. / / e. f. 77
18 Missing Addend Problems and Fact Families Nathalie needs ten safetypins. She only has two. How many more does she need? +? 2 + = 10 You can solve 2 + = 10 with subtraction: 2 + = = The answer to both problems is 8! Use the Fact Family: = 10, 10 2 = = 10, 10 8 = 2 1. Fill in. Note you can use the facts from the same fact family in each case. a. +? 5 + = = d. +? 5 + = = g. +? 3 + = = b. +? 3 + = = e. +? 4 + = = h. +? 2 + = = c. +? 4 + = = f. +? 5 + = = i. +? 1 + = = 86
19 Chapter 3: Addition and Subtraction Facts Introduction The third chapter of Math Mammoth Grade 1A Complete Worktext provides lots of practice for learning and memorizing the basic addition and subtraction facts within Memorizing the facts The lessons named, Addition and Subtraction Facts With..., aim at helping your child to memorize the basic facts within We approach it from the concept of 'fact families', which makes the process to be logical and structured. These lessons have a lot of repetition and practice for both subtraction and addition facts. Some children may not need all the practice. Use your judgment and skip some pages in this section if you feel necessary. You can also "save" some of the pages to be completed later, as a review. Alongside this book, you can also use math games or flashcards to reinforce these facts. You can find a list of some free online games at National Council of Teachers of Mathematics (NCTM) recommends in their Grade 2 Curriculum Focal Points that children "...develop quick recall of basic addition facts and related subtraction facts". This suggests that memorizing the addition and subtraction facts is not yet completely essential on first grade. It is advisable though to learn these facts fairly well at this point, because children will soon start learning adding those singledigit numbers where the sum is more than ten. Mathematics builds upon previously learned concepts and facts. Learning addition and subtraction facts is essential for later study. So if your child does not memorize these facts yet, don't worry. Go on with your curriculum, but keep practicing the facts with games, worksheets, drill, etc. on the side until they get there. The Lessons in Chapter 3 page span Addition and Subtraction Facts with 4 and pages Addition and Subtraction Facts with pages Addition and Subtraction Facts with pages Addition and Subtraction Facts with pages Addition and Subtraction Facts with pages Addition and Subtraction Facts with pages Adding and Subtracting Many Numbers pages Review  Facts with 6, 7, and pages Review  Facts with 9 and pages 90
20 Addition and Subtraction Facts with 8 1. Write the fact families in which the sum is eight. 8,, 8,, 8,, = 8 + = 8 8 = = 7 + = 8 + = 8 8 = = + = + = = =,, 8,, 8 + = 8 + = 8 = = + = 8 = 2. Write down the addition facts with 8 and memorize them! 0 + = = = 8 or or or + 0 = = 8 + = = = 8 or + = 8 99
21 Review Facts with 9 and Write addition and subtraction facts with 9 and = 9 9 = = = = 9 9 = 8 + = = 8 + = 9 9 = 7 + = = 7 + = 9 9 = 6 + = = 6 + = 9 9 = = = 5 2. a. Draw a line to connect each pair of numbers that add up to 9. Which number is left by itself? b. Draw a line to connect each pair of numbers that add up to 10. Which number is left by itself? Fill in the missing numbers. Draw a line to connect the facts that are from the same fact family. 9 = 7 9 = = 9 = = = = = = = 9 = = 9
22 4. Write an addition sentence or a subtraction sentence or a missing addend sentence. a. Millie bought two packs of crayons. Ken bought seven packs. How many more packs did he buy than she did? b. Mike has three yellow toy cars, four blue cars, and three red cars. How many cars does he have altogether? c. There were four birds in a tree. Four more flew in. Later, five of them flew away. How many birds were there in the tree to begin with, how many after the new ones flew in, and how many after some of them left? d. Elisa knows she has 10 crayons. She can only find four. How many are missing? e. A 10piece puzzle has two pieces missing. How many pieces are there now? 5. Fill in the missing numbers. Draw a line to connect the facts that are from the same fact family. 10 = 8 10 = 0 10 = 5 10 = = 10 6 = + 9 = = = = = = = = 10 4 = + 3 = = 8 10 = 0 115
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24 Contents Chapter 4: Place Value Within Introduction... 5 Counting in Groups of Naming and Writing Numbers The "Teen" Numbers Building Numbers A 100Chart Practicing Numbers Building Numbers Practicing Numbers Which Number is Greater? SkipCounting Mystery Numbers and More Practice Review Chapter 5: Clock Introduction Whole and Half Hours The Minutes AM and PM Review  Half Hours Chapter 6: Shapes and Measuring Introduction Shapes Shapes Measuring Lines in Inches Measuring Lines in Centimeters Review
25 Chapter 7: Adding and Subtracting Within Introduction Refresh Your Memory Adding Within the Same Ten Subtracting Within the Same Ten Whole Tens Difference and Word Problems Graphs Adding in Columns Subtracting in Columns Completing the Ten Going Over to the Next Ten Subtract to Ten Addition Practice Subtraction Review Chapter 8: Coins Introduction Money  Counting Dimes, Nickels, and Cents Money  Counting Dimes, Nickels, and Cents Quarters, Too Practicing With Money Review  Coins
26 Counting in Groups of Count in groups of TEN. Count ten dots, and circle them. Write how many tengroups you get. Write how many ones are left over. a. tengroups ones b. tengroups ones c. tengroups ones d. tengroups ones e. tengroups ones f. tengroups ones 2. Counting game 1. (Optional  to give more practice for making tengroups) Toss a bunch of beans or other objects on a table, and ask the child to make tengroups. Then ask the child to count the tengroups and the individual ones, using "fourtens six" or "seventens one", etc. Repeat as necessary with a different amount of objects, taking turns. 8
27 3. Counting game 2. You need: Counting items, such as sticks, beads, or beans. Small bags or bowls, OR rubber bands if using sticks. Before the game: Place 10 of the items in the middle, and the rest in a pile on the side. Play: At his turn, each player adds one more item to the middle pile on the table, and names the number thus formed. Whenever a whole ten is fulfilled, those ten items are grouped together with a rubber band or by placing them in a small bag or bowl. ONLY use words one to ten when counting in this came. Words like eleven, thirteen, twenty, fifty etc. are not allowed. For example, eleven is said as "ten and one", twelve is "ten and two", twenty is "two tens", twentyfive is "two tens and five", etc. Variation: Each player adds two (or some other quantity) matches to the pile instead of one. 4. Introduce the 100bead abacus to the student. Make these numbers with the 100bead abacus. a. 6 tens 5 ones b. 2 tens 7 ones c. 7 tens d. 1 ten 5 ones e. 2 tens 1 one f. 8 tens 9 ones g. 9 tens 3 ones h. 1 ten 1 one i. 4 tens 6 ones j. 6 tens k. 7 tens 1 one l. 1 ten 8 ones 5. Take turns telling each other what number to make on the abacus, such as "7 tens 9" or "1 ten 7". Do not proceed further until the student has mastered this! This is crucial. The names of the numbers with whole tens are: ten = ten four tens = forty seven tens = seventy two tens = twenty five tens = fifty eight tens = eighty three tens = thirty six tens = sixty nine tens = ninety ten tens = hundred 6. Say the number names from ten to hundred aloud a few times, while also making them with the 100bead abacus. It almost sounds like a rhyme! 9
28 Building Numbers Fill in the table. Think of the '+' sign as "and": means 10 and 3. a. Eleven b. c. Thirteen d. 1 ten 1 one 1 ten 2 ones 1 ten ones 1 ten ones tens ones tens ones tens ones tens ones e. f. Sixteen g. h tens ones tens ones tens ones tens ones i. j. Twenty k. Twentyone l tens ones tens ones tens ones tens ones
29 Which Number is Greater? 1. Fill in the missing parts. Circle the number that is more. OR OR 3 tens 6 ones tens ones tens ones tens ones 36 OR OR tens ones tens ones tens ones tens ones Study the above pictures. Do we first check how many TENS the numbers have or how many ONES the numbers have? Check first how many the numbers have. If the numbers have the same amount of, then compare the. For example, 92 has more TENS than 89, so 92 is greater than has the same amount of TENS as 66, but it has less ONES than 66. Therefore 62 is less than 66. The symbol > means "greater than", and < means "less than". The open end or open mouth of the symbol ALWAYS points to the bigger number. For example: 3 < 5 14 > 3 60 > < 99 7 < 17 Since 44 comes before 47 when you read the number line from left to right, 44 <
30 2. Write < or > between the numbers to compare them. a. 80 < 88 c e g b d f h Write < or > between the numbers. You can draw tensticks and onedots to help. a b c d e f g h i
31 SkipCounting 1. Fill in the chart. Then color yellow every second number on the number chart starting at 2. What pattern do you notice? Fill in the chart. Then color blue every second number on the number chart starting at 1. What pattern do you notice?
32 5. Write the time yourself! a. b. c. d. e. f. g. h. 6. On the first row, write the time. On the second row, draw the hour hand. to show the time a halfhour later. On the third row, draw the hour hand to show the time an hour later from the first row of clocks. Write the time. a. b. c. d. A halfhour later An hour later 39
33 The Minutes and Half Hours The minute hand on the clock is the thinner and longer hand. It shows us the minutes  but the numbers 112 on the clock face do NOT tell us the minutes. The green numbers are for the minute hand. They are not normally written on the clock face at all. The time on the clock is 4 o'clock, or 4:00, or four hours and zero minutes. Find a clock that has a knob you can turn to move the hour and minute hands. Set the hour hand pointing to one, and the minute hand pointing straight "up". Move the hour hand from 1 to 2, and observe the minute hand! Do it again: move the hour hand from 2 to 3. What does the minute hand do? Make the minute hand travel backwards as well. If you make the hour hand travel from 7 to 10, how many 'rounds' does the minutehand make? It is 1 o'clock (and 0 minutes) 1. You know these from the previous lesson. But now the minute hand is added. Write the time using the expressions o'clock and half past. a. b. c. d. 41
34 3. Repeat the patterns to fill the grids. 54
35 Measuring Lines in Centimeters You can find out how long things are in inches, but you can also use centimeters. This line is 1 centimeter long: (This line is 1 inch long. ) 5 centimeters is about as long as 2 inches Centimeter is written shortly as "cm". 1. How many centimeters long are these things? cm cm cm cm 2. How many centimeters? Measure the line segments with your centimeterruler. 61
36 Adding Within the Same Ten Remember how numbers are broken down into TENS and ONES: 23 = = Break the numbers into tens and ones. 2. Do this the other way around! a. 18 = b. 30 = + a = b = 25 = + 67 = = = 89 = + 90 = = = 55 = + 46 = = = tens ones Write tens and ones in columns. Add the tens in their column. Add the ones in their column. (The box with 'T' is a ten.) 3. Add the tens and ones in their own columns. tens ones tens ones a. + b. + tens ones tens ones c. + d. + 65
37 2. Difference is also how many more! Find the differences in the way that is easier for you. a. Difference of 10 and 50: b. Difference of 20 and 70: c. How many more is 14 than 10? d. How many more is 20 than 6? 10 + = = = = = = = 20 6 = e. How many more is 80 than 40? f. How many more is 16 than 10? g. Difference of 50 and 48: h. Difference of 100 and 99: 3. Write a missing addend sentence or a subtraction sentence for each problem and solve. a. Jane had 20 strawberries and Jonathan had 11. How many more did Jane have? Jane had 9 more = = 9 b. One ruler is 30 cm long, and another rule is 10 cm long. How many centimeters longer is the first one? c. One book is 14 cm wide, and another is 6 cm wide. How many centimeters wider is the first book? d. Ann had five toy cars in a game, and Judith had 10. Then Ann got two more. Now who has more cars? How many more? e. Jake had 6 dollars and Jim had 12. Then, Jake earned 10 dollars. Now who has more money? How many dollars more? 76
38 2. Write the previous and next whole ten. a. 10, 13, 20 b., 94, c., 4, d., 93,, 25,, 39,, 57,, 81,, 78,, 65,, 72,, 46, 3. Complete the next ten. Below, write the same kind of problem within numbers a = 30 b = c = d = 3 + = = 7 + = 4 + = e = f = g = h = 5 + = 1 + = 9 + = + = 4. Complete the tens. Think of the corresponding problem within range a. b. c. d = = = = = = = = = = = = Count by fives. a. 10, 15,,,,,,,,,,, b. 1, 6,,,,,,,,,,, c. 17, 22,,,,,,,,,,, d. 13, 18,,,,,,,,,,, 85
39 Counting Dimes, Nickels, and Cents This coin is called one cent or one penny. We write 1. This coin is called one dime. It is worth ten cents Count up when finding how many cents total: Two dimes is 20. Four pennies is 4. The total is 24 cents. 1. Count and write the total amount in cents. a. b. c. d. 102
40 Quarters One quarter is 25 cents. The word "quarter" means onefourth. A quarter coin is onefourth part of a dollar. One dollar is 100 cents, and is written $1. = 4 quarters 1 dollar = dollar = $1 Two quarters = 50. Three quarters = , 45, 55 (count dimes by tens) 56, 57 Count the quarters first since they have the biggest centvalue. 1. Quarters and dimes. Write the total amount in cents. a. b. c. d. e. f. g. h. i. 107
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