Contents
Foreword .............................................................................
5
Chapter 1: Addition Within 0-10
Introduction ............................................................................
6
Two Groups and a Total ....................................................... 10
Learn Symbols + and = ......................................................... 13
Addition Practice ................................................................... 15
Which is More? .....................................................................
17
Missing Items ......................................................................... 19
Sums with 5 ............................................................................ 22
Sums with 6 ............................................................................ 24
Adding on a Number Line .................................................... 26
Sums with 7 ............................................................................ 30
Sums with 8 ............................................................................ 33
Addition Practice ................................................................... 36
Sums with 9 ............................................................................ 39
Sums with 10 .......................................................................... 43
Some Symbols ........................................................................
47
Review of Addition Facts ...................................................... 50
Chapter 2: Subtraction Within 0-10
Introduction ............................................................................. 54
Subtraction is 'Taking Away' ................................................ 57
Count Down to Subtract ........................................................ 60
Subtraction and Addition in the Same Picture .................... 64
When Can You Subtract? ..................................................... 68
Subtraction and Addition ...................................................... 72
Two Parts — One Total ........................................................ 75
Fact Families ........................................................................... 77
How Many More? .................................................................. 80
Difference or How Many More? ............................................ 83
Missing Addend Problems and Fact Families ..................... 86
Review ..................................................................................... 89
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Chapter 3: Addition and Subtraction Facts
Introduction ........................................................................... 90
Addition and Subtraction Facts with 4 and 5 ...................
92
Addition and Subtraction Facts with 6 ..............................
94
Addition and Subtraction Facts with 7 ..............................
97
Addition and Subtraction Facts with 8 ..............................
99
Addition and Subtraction Facts with 9 .............................. 102
Addition and Subtraction Facts with 10 ............................ 105
Adding and Subtracting Many Numbers ........................... 108
Review — Facts with 6, 7, and 8 .......................................... 112
Review — Facts with 9 and 10 ............................................. 114
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4
Foreword
Math Mammoth Grade 1-A and Grade 1-B 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 step-by-step 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
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5
Chapter 1: Addition Within 0-10
Introduction
The first chapter of Math Mammoth Grade 1-A Complete Worktext covers addition concept and addition
facts within 0-10.
The chapter starts out with very easy addition problems within 0-5, 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 1 + 5 =
__. 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 many-fold:
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.
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6
Two Groups and a Total
1. Separate the balls into two groups.
4
4
4
1 and 3
2 and 2
3 and 1
5
5
5
3 and 2
2 and 3
1 and 4
2. Separate the balls into two groups. Write how many are in the second group.
4
a.
1 and ___
5
d.
4 and ____
5
g.
1 and ____
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b.
4
2 and ____
e.
5
3 and ____
h.
5
2 and ____
10
c.
4
3 and ____
f.
5
2 and ____
i.
5
0 and ____
Learn Symbols + and =
3
+
2
=
5
1
THREE plus TWO equals FIVE
+
3
=
ONE plus THREE equals FOUR
1. Add. Read the addition sentences aloud using 'plus' and 'equals'.
a.
c.
b.
1+3=
___ + ___ =
1+2=
d.
e.
___ + ___ =
f.
___ + ___ =
___ + ___ =
i.
g.
h.
___ + ___ = ___
j.
___ + ___ = ___
k.
___ + ___ = ___
___ + ___ = ___
l.
___ + ___ = ___
___ + ___ = ___
n.
m.
___ + ___ = ___
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o.
___ + ___ = ___
13
___ + ___ = ___
Addition Practice
1. Draw more in the second group, and add.
2 + 1 = ___
3 + 2 = ___
1 + 2 = ___
4 + 1 = ___
2 + 3 = ___
0 + 4 = ___
2 + 2 = ___
1 + 0 = ___
3 + 1 = ___
2 + 2 = ___
1 + 3 = ___
0 + 5 = ___
4 + 1 = ___
2 + 3 = ___
1 + 3 = ___
2. Draw dots. Add.
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15
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!
1 + ___ = 5
There should be 5 dots in all.
Draw 4 in the second die face.
1 + 4 makes 5.
Read: "2 plus what number makes 4?"
"2 and how many more makes 4?"
2 + ___ = 4
1. Draw more dots.
1 + ___ = 3
2 + ___ = 3
4 + ___ = 5
3 + ___ = 5
2 + ___ = 5
3 + ___ = 4
5 + ___ = 5
1 + ___ = 4
2 + ___ = 4
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19
Sums with 6
1. Six hippos are grouped into two groups, in different ways. Write the addition sentences.
|
|
|
|
|
|
|
2.Add.
2+4=
1+5=
3+3=
1+4=
2+3=
3+2=
2+4=
1+5=
2+2=
4+2=
4+2=
3+3=
3+3=
2+2=
2+2=
2+2=
3. Drill. Don't write the answers but just think in your head.
1+
=6
4+
=6
+2=6
+3=6
2+
=6
3+
=6
+0=6
+1=6
6+
=6
5+
=6
+4=6
+5=6
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24
Adding on a Number Line
5+3=8
First jump 5...
Then jump 3 more.
You land at 8.
1. Draw jumps to illustrate the addition and find the answer.
You can use two different colors to draw the jumps.
a.
5 + 2 = ___
b.
4 + 1 = ___
c.
6 + 3 = ___
d.
9 + 1 = ___
e.
7 + 3 = ___
f.
4 + 3 = ___
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26
Sums with 9
1. Nine balls are grouped into two groups, in different ways. Write the addition sentences.
|
|
|
|
|
|
|
|
|
|
2. Add.
5+4=
2+6=
3+6=
1+6=
4+5=
3+4=
2+7=
3+5=
1+8=
4+4=
3. Drill. Don't write the answers here. Just think in your head.
+8=9
+4=9
2+
=9
3+
=9
+2=9
+6=9
9+
=9
6+
=9
+1=9
+7=9
+3=9
0+
=9
4+
=9
+5=9
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39
7+
=9
Some Symbols
= means
"EQUAL".
6=2+4
7=7
Seven equals seven.
Six equals two plus four.
≠ means
"NOT EQUAL".
7≠8
3+4≠5
Seven is not equal to eight.
Three plus four is not equal to five.
1. Equal or not? Write = or ≠ . Read the sentences aloud.
1 ≠ 2
4+1
5
7
4+4
6
2+3
8
7
2+5
7
5
5+0
4
5+5
3
1
2+2
3
9
9
2
2+2
2. Pick a number for the blank line so the comparison is true.
5 6 7
4 5 6
5 6 7
2 3 4
___ < 6
___ < 5
___ > 6
___ > 3
9 7 5
3 6 9
1 3 7
2 4 6
___ > 7
___ < 5
___ > 6
___ < 3
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47
Chapter 2: Subtraction Within 0-10
Introduction
The second chapter of Math Mammoth Grade 1-A 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 take-away 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 9 - 5 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:
z
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.
z
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
Subtraction is 'Taking Away'
From five bananas we take away three.
5–3
Five minus three
There are two left.
=
equals
From six carrots we take away one.
6–1
Six minus one
2
two
There are five left.
=
equals
5
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?
a.
10 – 4 = ____
8 total, cross out 7.
d.
8 – 7 = ____
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6 total. Cross out 6.
How many are left?
b.
6 – 6 = ____
8 total, cross out 6.
e.
8 – 6 = ____
57
8 total. Cross out 2.
How many are left?
c.
8 – 2 = ____
7 total, cross out 3.
f.
7 – 3 = ____
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 – ___ = ___
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64
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:
2+3=5
5–3=2
3+2=5
5–2=3
1. Write the fact families to match the pictures.
6
8
/
a.
/
1 + 5 = 6
6 – ___ = ___
5 + 1 = 6
6 – ___ = ___
b.
__
__
/
/
c.
d.
__
__
/
/
e.
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f.
77
Missing Addend Problems and Fact Families
Nathalie needs ten safety-pins. She only has two.
How many more does she need?
+
2 +
?
= 10
You can solve 2 + ___ = 10 with subtraction:
2 + ___ = 10
10 – 2 = ___
Use the Fact Family:
2 + 8 = 10, 10 – 2 = 8
8 + 2 = 10, 10 – 8 = 2
The answer to both problems is 8!
1. Fill in. Note you can use the facts from the same fact family in each case.
+ ?
a.
+?
b.
+?
c.
5 + ___ = 7
3 + ___ = 8
4 + ___ = 9
7 – 5 = ___
8 – 3 = ___
9 – 4 = ___
+?
d.
+?
e.
+?
f.
5 + ___ = 10
4 + ___ = 7
5 + ___ = 8
10 – 5 = ___
7 – 4 = ___
8 – 5 = ___
g.
+?
+?
h.
i.
+?
3 + ___ = 10
2 + ___ = 9
1 + ___ = 7
10 – 3 = ___
9 – 2 = ___
7 – 1 = ___
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86
Chapter 3: Addition and Subtraction Facts
Introduction
The third chapter of Math Mammoth Grade 1-A Complete Worktext provides lots of practice for learning
and memorizing the basic addition and subtraction facts within 0-10.
Memorizing the facts
The lessons named, Addition and Subtraction Facts With ..., aim at helping your child to memorize the
basic facts within 0-10. 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 www.homeschoolmath.net/math_resources_2.php
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 single-digit 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 5 ..... 92
2 pages
Addition and Subtraction Facts with 6 ..............
94
3 pages
Addition and Subtraction Facts with 7 ..............
97
2 pages
Addition and Subtraction Facts with 8 ..............
99
3 pages
Addition and Subtraction Facts with 9 .............. 102
3 pages
Addition and Subtraction Facts with 10 ............ 105
3 pages
Adding and Subtracting Many Numbers ........... 108
4 pages
Review - Facts with 6, 7, and 8 .......................... 112
2 pages
Review - Facts with 9 and 10 ............................. 114
2 pages
90
Addition and Subtraction Facts with 8
1. Write the fact families in which the sum is eight.
8, __, 8
___, ___, 8
___, ___, 8
8 + 0 = 8
7 + ___ = 8
___ + ___ = ___
___ + ___ = 8
___ + ___ = 8
___ + ___ = ___
8 – ___ = ___
8 – ___ = ___
___ – ___ = ___
___ – ___ = ___
___ – ___ = ___
___ – ___ = ___
___, ___, 8
___, ___, 8
___ + ___ = 8
___ + ___ = 8
___ + ___ = 8
___ – ___ = ___
___ – ___ = ___
___ – ___ = ___
2. Write down
the addition facts
with 8 and
memorize them!
0 + ___ = 8
or
___ + 0 = 8
1 + ___ = 8
or
___ + 1 = 8
2 + ___ = 8
or
___ + ___ = 8
3 + ___ = 8
or
___ + ___ = 8
4 + ___ = 8
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99
Review — Facts with 9 and 10
1. Write addition and subtraction facts with 9 and 10.
0 + ___ = 9
9 – ___ = 9
1 + ___ = 10
10 – ___ = 9
1 + ___ = 9
9 – ___= 8
___ + ___ = 10
10 – ___ = 8
___ + ___ = 9
9 – ___= 7
___ + ___ = 10
10 – ___ = 7
___ + ___ = 9
9 – ___= 6
___ + ___ = 10
10 – ___ = 6
___ + ___ = 9
9 – ___= 5
5 + ___ = 10
10 – ___ = 5
2. a. Draw a line to connect each pair of
numbers that add up to 9.
Which number is left by itself?
0
7
2
1
b. Draw a line to connect each pair of
numbers that add up to 10.
Which number is left by itself?
2
8
3
5
2
6
9
7
1
4
3
4
9
5
8
9
6
4 0
2
5
1
7
10
3
8
6
1
9
7
3
8
6
3. Fill in the missing numbers. Draw a line to connect the facts that are from
the same fact family.
9 – ___ = 7
___ + 2 = 9
9 – ___ = 5
9 – ___ = 6
8 + ___ = 9
9 – 6 = ___
9 – 1 = ___
___ + 5 = 9
9 – ___ = 2
9 – ___ = 4
3 + ___ = 9
___ + 8 = 9
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114
5
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 10-piece 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
___ + 9 = 10
___ + 1 = 10
___ – 10 = 0
4 + ___ = 10
10 – 5 = ___
10 – ___ = 5
5 + ___ = 10
10 – 4 = ___
10 – ___ = 1
2 + ___ = 10
___ + 3 = 10
10 – 3 = ___
___ + 7 = 10
10 – ___ = 8
10 – 6 = ___
___ + 10 = 10
10 – ___ = 0
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115