GRADE 2 MODULE 1 STUDENT WORKBOOK NYS COMMON …
Transcript of GRADE 2 MODULE 1 STUDENT WORKBOOK NYS COMMON …
NYS
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GRADE 2MODULE 1
STUDENT WORKBOOK
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Math Workbook
Grade 2
Module # 1
Name: _____________
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A B C C D E F G H I J E KL M N O P Q Q P L O P R S Q T U V S Q T U W O N O X R R W O X Y X Q Z [ F
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A B C C D E F \ I D ] ^ B _ G B KL M N O P Q Q P L O P R S Q T U V S Q T U W O N O X R R W O X Y X Q Z [ FName Date
1. Add or subtract. Complete the number bond for each set. 3 + 7 = ____ 9 + 1 = ____ 7 + 3 = ____ 1 + 9 = ____ 10 – 7 = ____ 10 – 1 = ____ 10 – 3 = ____ 10 – 9 = ____
2. Circle all the number sentences that are true.
0 + 10 = 10 6 + 3 = 10 5 + 5 = 10 9 + 1 = 10 2 + 9 = 10 6 + 4 = 10 3 + 7 = 10 1 + 10 = 10
3. Fill in the missing numbers.
4 + ___ = 10 10 – 6 = ___ 10 = ___ + 6 ___ = 10 – 4
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A B C C D E F \ I D ] ^ B _ G B KL M N O P Q Q P L O P R S Q T U V S Q T U W O N O X R R W O X Y X Q Z [ F10
6
10
7 9
1
4. Complete the number bonds. 5. Jim had $6 in the bank. He found some money on a park bench and put it the bank.
He now has $10 in the bank. How much money did he find?
6. Natasha was given some money for her birthday. She spent $7 on a bow and $3 on a hair clip. If she used all of her money, how much money was Natasha given? Solve using words, math drawings, or numbers.
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A B C C D E F b c J K d J e f B KL M N O P Q Q P L O P R S Q T U V S Q T U W O N O X R R W O X Y X Q Z [ F
0 1
2 3
5
4
Name Date
Complete each number bond to make 10. Write at least one addition and one subtraction sentence to accompany each bond.
____ + ____ = ____ ____ + ____ = ____
____ - ____ = ____ ____ - ____ = ____
____ + ____ = ____ ____ + ____ = ____
____ - ____ = ____ ____ - ____ = ____
____ + ____ = ____ ____ + ____ = ____
____ - ____ = ____ ____ - ____ = ____
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A B C C D E F h i _ ] B I j D E k d B _ H ^ l K BL M N O P Q Q P L O P R S Q T U V S Q T U W O N O X R R W O X Y X Q Z [ FName Date
Draw all the number bonds of 10. The first one is done for you.
10
10 0
10
10 0
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m n o o p q r s t u v w x y z { w | { } x ~ � � � | } y � � � w x � � � � u � y { � | u � � � } x � } � y � u x ~ u � � � �� } } x w � � � w � � } | ~ � | } { � w z � �� � � n s � � � � � � � � � � � �� � � � � � � � � � � � ¡ ¢ £ ¤ ¥ ¦ § ¨ ¨ ¡ © ª « ¬ ¡ ¢ ¢ ¡ ® ¢ ¯ ¦ ° ± ² ² ± ³ ° ± ´ µ ¶ ± ´ ·
¸ ¹ º º » ¼ ½ ¾ ¿ » À Á ¹ Â Ã ¹ ÄÅ Æ Ç È É Ê Ê É Å È É Ë Ì Ê Í Î Ï Ì Ê Í Î Ð È Ç È Ñ Ë Ë Ð È Ñ Ò Ñ Ê ½ Ó ÔName Date
1. Complete the number bonds
2. Find the unknown numbers that make the number sentences true.
9 – 5 = 8 – 5 =
3 + = 8 3 + = 7
8 – = 4 6 – = 3
18 = + 10 17 = 7 +
– 5 = 4 – 6 = 3
3. Maria put some cups on the table. Jesse put 7 more. There were 17 cups in all.
How many cups did Maria put on the table? Show your thinking using words, math
drawings, or numbers.
7
3
9 7
6
8
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! " " # $ % & ' # ( ) ! * + ! ,- . / 0 1 2 2 1 - 0 1 3 4 2 5 6 7 4 2 5 6 8 0 / 0 9 3 3 8 0 9 : 9 2 % ; Ô4. Fill in the missing numbers:
11 is and 1 13 is and 3
15 is 10 and 10 and is 19
10 and 8 is 12 is 10 and
5. Your older sister says, “3 + 10 is easy”. You can hear the answer when you count the
Say Ten way. Use the ten-frame cards to show why this strategy works for
10 + 7 = 17.
6. Maggie had a bag of marbles. There were 5 yellow marbles, 6 white marbles and 4
blue marbles. How many marbles were there in all? Show your thinking using words,
math drawings, or a number sentence.
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! " " # $ % = > ? , @ ? A B ! ,- . / 0 1 2 2 1 - 0 1 3 4 2 5 6 7 4 2 5 6 8 0 / 0 9 3 3 8 0 9 : 9 2 % ; ÔName Date
1. 7 – 4 =
2. 2 + = 8
3. 6 = 9 –
4. Mr. Gardener has a box with 12 tomatoes. He gives 2 tomatoes to his sister and another 7 tomatoes to his neighbor. How many tomatoes does he have left? Show your work with a picture and number sentence.
Mr. Gardener has tomatoes.
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1. Solve the facts by recording make ten solutions with number bonds. Then draw a
line connecting each one with the number sentence showing how you added the
remaining ones to ten. The first one is done for you.
8 + 3 = 10 + 4
^
2 + 1
8 + 6 = 10 + 3
9 + 4 = 10 + 1
6 + 5 = 10 + 2
8 + 8 = 10 + 1
5 + 7 = 10 + 6
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� � � � � � � Å � � Æ Ç � È � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �2. Fill in the blank to make the sentence true.
a. 5 + = 15
b. 4 + = 15
c. + 9 = 16
d. 9 + 7 =
e. + 4 = 10 + 3
f. 6 + = 10 + 4
3. Margaret went to camp for 8 hours on Saturday and 4 hours on Sunday. Sandra went
to camp for 6 hours on Saturday and 5 hours on Sunday.
a. How many hours did Margaret spend at camp?
b. How many hours did Sandra spend at camp?
4. Draw to explain how to add 9 and 4 by making ten.
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1. Draw to explain 8 + 6 = 10 + 4.
2. Solve.
a. 9 + 7 = + 6
b. + 3 = 10 + 2
c. 7 + = 10 + 1
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� � � � � � ! " � # $ � % & � '( ) * + , - - , ( + , . / - 0 1 2 / - 0 1 3 + * + 4 . . 3 + 4 5 4 - 6 7 8Name Date
Use basic facts to help you solve with mental math.
1. 13 + 2 =
2. 11 + 4 =
3. 14 + = 16
4. 13 + 6 =
5. = 12 + 4
6. + 3 = 17
7. 19 = + 13
8. 15 – 3 =
9. 15 – 4 =
10. 15 – = 13
11. 17 – 5 =
12. = 18 – 2
13. – 2 = 17
14. 14 = – 5
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� � � � � � ! " � # $ � % & � '( ) * + , - - , ( + , . / - 0 1 2 / - 0 1 3 + * + 4 . . 3 + 4 5 4 - 6 7 815. Circle the number sentences that are true.
13 = 10 + 2
13 + 7 = 17 + 3
13 – 2 = 10 + 1
12 + 5 = 17 + 1
16. Autumn made some cookies. She ate 4 of them and had 16 left. How many did she
make?
17. Mrs. Parker read 12 books last year. So far this year she has read three books.
How many books has she read altogether?
18. Andy had $48. He spent $5 on a book and gave $3 to his brother. How much money
did he have left?
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� � � � � � ~ � � ' � � � � � '( ) * + , - - , ( + , . / - 0 1 2 / - 0 1 3 + * + 4 . . 3 + 4 5 4 - 6 7 8Name Date
Solve the problems. Write the basic fact that helps you solve each one. The first one
is done for you.
1. 14 – 1 = 13
Basic Fact: 4 – 1 = 3
2. 14 + 1 =
Basic Fact:
3. 15 + 3 =
Basic Fact:
4. 18 + 2 =
Basic Fact:
5. 17 – 6 =
Basic Fact:
6. 19 + 7 =
Basic Fact:
7. 16 + 4 =
Basic Fact:
8. 12 + 8 =
Basic Fact:
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¢ £ ¤ ¤ ¥ ¦ § ¨ © ª « ¬ ® ¬ ¯ ª ° ¬ ¯ ± ² ° ³ ´ « ° µ ³ ¬ ´ ° ª ¶ · ¸ ª ¶ ¯ ± ² ° ³ ´ « ° ¹ ¶ º · ¹ ° ¸ ¹ ¶ » ¼ ´ ¶ ½´ ® ® ¾ ¿ ° ¬ ¬ ¶ ª À ¯ ° ª ® · ¬ ³ ½ ® ³ ¬ ² ¾ ª ¯ ÁÂ Ã Ä £ ¨ Å Æ Ç Æ È É Ê Ë Ì Ë Í ÎÏ Ð Ñ Ò Ð Ó Ô Õ Õ Ô Ö Ó Ô × Ø Ù Ú Ö Û Ü Ý Þ Þ × ß à á â ã × Ø ã Ø × ä Ø å Ü æ ç è è ç é æ ç ê ë ì ç ê í
Name Date
1. Solve the following problems. Circle the number sentence if you must subtract from
the ten.
10 – 2 = 10 – 7 = 10 – 4 =
11 – 2 = 11 – 7 = 11 – 4 =
12 – 2 = 12 – 7 = 12 – 4 =
13 – 2 = 13 – 7 = 13 – 4 =
14 – 2 = 14 – 7 = 14 – 4 =
15 – 2 = 15 – 7 = 15 – 4 =
16 – 2 = 16 – 7 = 16 – 4 =
17 – 2 = 17 – 7 = 17 – 4 =
18 – 2 = 18 – 7 = 18 – 4 =
19 – 2 = 19 – 7 = 19 – 4 =
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î ï ð ð ñ ò ó ô õ ñ ö ÷ ï ø ù ï úû ü ý þ ÿ � � ÿ û þ ÿ � � � � � � � � � � � þ ý þ � � � � þ � � � � ¡
¢ £ ¤ ¤ ¥ ¦ § ¨ © ª « ¬ ® ¬ ¯ ª ° ¬ ¯ ± ² ° ³ ´ « ° µ ³ ¬ ´ ° ª ¶ · ¸ ª ¶ ¯ ± ² ° ³ ´ « ° ¹ ¶ º · ¹ ° ¸ ¹ ¶ » ¼ ´ ¶ ½´ ® ® ¾ ¿ ° ¬ ¬ ¶ ª À ¯ ° ª ® · ¬ ³ ½ ® ³ ¬ ² ¾ ª ¯ ÁÂ Ã Ä £ ¨ Å Æ Ç Æ È É Ê Ë Ì Ë Í �Ï Ð Ñ Ò Ð Ó Ô Õ Õ Ô Ö Ó Ô × Ø Ù Ú Ö Û Ü Ý Þ Þ × ß à á â ã × Ø ã Ø × ä Ø å Ü æ ç è è ç é æ ç ê ë ì ç ê í
2. Fill in the blank to make the number sentence correct.
11 – 8 = 2 +
14 – 5 = 5 +
17 – 8 = 2 +
16 – 9 = 1 +
13 – 7 = 3 +
18 – 4 = 6 +
3. Susan has a new pack of 10 pencils and 4 pencils from an old pack. She gave 6
pencils from the new pack to her brother. How many pencils does she have left?
4. Marco brought his marble collection to school. He has 11 blue marbles and 7 red
marbles. At school, Marco lost 3 of his blue marbles.
a. How many blue marbles does he have now?
b. How many marbles does he have left?
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¢ £ ¤ ¤ ¥ ¦ § ¨ © ª « ¬ ® ¬ ¯ ª ° ¬ ¯ ± ² ° ³ ´ « ° µ ³ ¬ ´ ° ª ¶ · ¸ ª ¶ ¯ ± ² ° ³ ´ « ° ¹ ¶ º · ¹ ° ¸ ¹ ¶ » ¼ ´ ¶ ½´ ® ® ¾ ¿ ° ¬ ¬ ¶ ª À ¯ ° ª ® · ¬ ³ ½ ® ³ ¬ ² ¾ ª ¯ ÁÂ Ã Ä £ ¨ Å Æ Ç Æ È É Ê Ë Ì Ë Í �Ï Ð Ñ Ò Ð Ó Ô Õ Õ Ô Ö Ó Ô × Ø Ù Ú Ö Û Ü Ý Þ Þ × ß à á â ã × Ø ã Ø × ä Ø å Ü æ ç è è ç é æ ç ê ë ì ç ê í
Name Date
Complete each set.
15 – 9 14 – 6 /\ /\ __ __ __ __ 10 – 9 = 10 – 6 =
1 + 5 = 4 + 4 =
15 – 9 = 14 – 6 =
11 – 8 12 – 7 /\ /\ __ __ __ __ 10 – = 10 – =
+ 1 = + 2 =
11 – 8 = 12 – 7 =
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[ \ ] ] ^ _ ` a b c d _ ef g h i j k k j f i j l m k n o p m k n o q i h i r l l q i r s r k t u v
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w x y y z { | } ~ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � �� � � x } � � � � � � � � � � � �� ¡ ¢ £ ¤ ¥ ¥ ¤ ¦ £ ¤ § ¨ © ª ¦ « ¬ ® ® § ¯ ° ± ² ³ § ¨ ³ ¨ § ´ ¨ µ ¬ ¶ · ¸ ¸ · ¹ ¶ · º » ¼ · º ½
¾ ¿ À À Á Â Ã Ä Å Á Æ Ç ¿ È É ¿ ÊË Ì Í Î Ï Ð Ð Ï Ë Î Ï Ñ Ò Ð Ó Ô Õ Ò Ð Ó Ô Ö Î Í Î × Ñ Ñ Ö Î × Ø × Ð Ù Ú vName Date
Add or subtract. Then write two more related problems for each basic fact.
2 + 4 = 6 – 4 =
12 + 4 = 36 – 4 =
22 + 4 = 56 – 4 =
Add or subtract.
1. 2 + 5 = 2. 7 – 5 =
3. 12 + 5 = 4. 27 – 5 =
5. 32 + 5 = 6. 47 – 5 =
7. 72 + 5 = 8. 87 – 5 =
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w x y y z { | } ~ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � �� � � x } � � � � � � � � � � � Û� ¡ ¢ £ ¤ ¥ ¥ ¤ ¦ £ ¤ § ¨ © ª ¦ « ¬ ® ® § ¯ ° ± ² ³ § ¨ ³ ¨ § ´ ¨ µ ¬ ¶ · ¸ ¸ · ¹ ¶ · º » ¼ · º ½
¾ ¿ À À Á Â Ã Ä Å Á Æ Ç ¿ È É ¿ ÊË Ì Í Î Ï Ð Ð Ï Ë Î Ï Ñ Ò Ð Ó Ô Õ Ò Ð Ó Ô Ö Î Í Î × Ñ Ñ Ö Î × Ø × Ð Ù Ú v9. 3 + 7 = 10. 10 – 7 =
11. 13 + 7 = 12. 20 – 7 =
13. 33 + 7 = 14. 50 – 7 =
15. 53 + 7 = 16. 70 – 7 =
Solve.
56 people visited the museum for a tour. 9 people had to leave before the tour was over. How many people were still at the museum for the tour?
Create at least two more sets of problems if you finish early.
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w x y y z { | } ~ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � �� � � x } � � � � � � � � � � � Ü� ¡ ¢ £ ¤ ¥ ¥ ¤ ¦ £ ¤ § ¨ © ª ¦ « ¬ ® ® § ¯ ° ± ² ³ § ¨ ³ ¨ § ´ ¨ µ ¬ ¶ · ¸ ¸ · ¹ ¶ · º » ¼ · º ½
¾ ¿ À À Á Â Ã Ý Þ ß Ê à ß á â ¿ ÊË Ì Í Î Ï Ð Ð Ï Ë Î Ï Ñ Ò Ð Ó Ô Õ Ò Ð Ó Ô Ö Î Í Î × Ñ Ñ Ö Î × Ø × Ð Ù Ú vName Date
Solve the problems. In the space provided, write a related problem for each of the
basic facts.
4 + 2 = 6 – 4 = 1 + 9 =
24 + 2 = 36 – 4 = 11 + 9 =
84 + 2 = 76 – 4 = 61 + 9 =
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ã ä å å æ ç è é ê ë ë ì í î ï í ð ñ ò ò ó ô í ð õ ö ÷ ø ö ù ÷ î í ù ô ø ú û ë ë í î í ø ð î ø ü û ý ù û î ù ð þÿ � � ä é � � � � ñ � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ! " # # " $ ! " % & ' " % (
) * + + , - . / 0 , 1 2 * 3 4 * 56 7 8 9 : ; ; : 6 9 : < = ; > ? @ = ; > ? A 9 8 9 B < < A 9 B C B ; D E FName Date
Solve the addition problems. Draw your bonds.
1. 78 + 4 = 2. 58 + 5 =
70 8 2 2
3. 54 + 6 = 4. 88 + 2 =
5. 26 + 8 = 6. 48 + 6 =
7. Fill in the blank to make the number sentences true.
9 + 1 = 8 + = 10
10 + 2 = 10 + = 15
19 + 3 = 8 + = 15
49 + 3 = 28 + = 30
69 + 3 = 30 + = 35
89 + 3 = 28 + = 35
27
G H I I J K L M N O O P Q R S Q T U V V W X Q T Y Z [ \ Z ] [ R Q ] X \ ^ _ O O Q R Q \ T R \ ` _ a ] _ R ] T bc d e H M f g h g U i j k l k m mn o p q o r s t t s u r s v w x y u z { | } } v ~ � � � � v w � w v � w � { � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � �� � � � � � � � � � � ¡ � ¢ £ ¤ ¡ � ¢ £ ¥ � � � ¦ ¥ � ¦ § ¦ � ¨ © ªLabel each number sentence as true or false.
8. 22 + 8 = 20 + 10
9. 57 + 5 = 50 + 10 + 2
10. 83 + 9 = 80 + 10 + 1
11. 68 + 7 = 70 + 5
12. 88 + 9 = 90 + 6
Solve.
Jorge saved 65 dollars last month. This month he saved 8 more dollars. How much
money does he have now?
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G H I I J K L M N O O P Q R S Q T U V V W X Q T Y Z [ \ Z ] [ R Q ] X \ ^ _ O O Q R Q \ T R \ ` _ a ] _ R ] T bc d e H M f g h g U i j k l k m «n o p q o r s t t s u r s v w x y u z { | } } v ~ � � � � v w � w v � w � { � � � � � � � � � � � � � �
� � � � � � � ¬ ® � ¯ ® ° ± � �� � � � � � � � � � � ¡ � ¢ £ ¤ ¡ � ¢ £ ¥ � � � ¦ ¥ � ¦ § ¦ � ¨ © ªName Date
Solve the following 4 problems. Show your number bonds. Draw if that will help you.
1. 28 + 4 = 2. 39 + 4 =
/\ /\
3. 27 + 9 = 4. 38 + 9 =
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Page Intentionally Left Blank
30
² ³ ´ ´ µ ¶ · ¸ ¹ º » ¼ ½ ¾ ¼ ¿ º À ¼ ¿ Á Â À Ã Ä » À Å Ã ¼ ½ Ä À º Æ Ç È º Æ ¿ Á Â À Ã Ä » À É Æ Ê Ç É À È É Æ Ë Ì Ì Ä Æ ÍÄ ¾ ¾ Î Ï À ¼ ¼ Æ º Ð ¿ À º ¾ Ç ¼ Ã Í ¾ Ã ¼ Â Î º ½ ¿ ÑÒ Ó Ô ³ ¸ Õ Ö × Ö Ë Ø Ù Ú Û Ú Ü ÝÞ ß à á ß â ã ä ä ã å â ã æ ç è é å ê ë ì í í æ î ï ð ñ ò æ ç ò ç æ ó ç ô ë õ ö ÷ ÷ ö ø õ ö ù ú û ö ù ü
ý þ ÿ ÿ � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �
31
� � � � � � � � ! " # $ % # & ! ' # & ( ) ' * + " ' , * # $ + ' ! - . / ! - & ( ) ' * + " ' 0 - 1 . 0 ' / 0 - 2 3 3 + - 4+ % % 5 6 ' # # - ! 7 & ' ! % . # * 4 % * # ) 5 ! $ & 89 : ; � � < = > = 2 ? @ A B A C CD E F G E H I J J I K H I L M N O K P Q R S S L T U V W X L M X M L Y M Z Q [ \ ] ] \ ^ [ \ _ ` a \ _ b
c d e e f g h i f j k e l d d mn o p q r s s r n q r t u s v w x u s v w y q p q z t t y q z { z s | } ~Name Date
1. Fill in the blanks to make the number sentences true. Draw number bonds to help
you subtract from the ten. The first two are done for you.
Example:
40 – 8 = 32 41 – 8 = ___
30 10 31 10
20 – 8 = ___ 21 – 8 = ___
30 – 8 = ___ 32 – 8 = ___
90 – 8 = ___ 91 – 8 = ___
20 – 9 = ___ 22 – 9 = ___
70 – 9 = ___ 71 – 9 = ___
40 – 5 = ___ 42 – 5 = ___
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� � � � � � � � ! " # $ % # & ! ' # & ( ) ' * + " ' , * # $ + ' ! - . / ! - & ( ) ' * + " ' 0 - 1 . 0 ' / 0 - 2 3 3 + - 4+ % % 5 6 ' # # - ! 7 & ' ! % . # * 4 % * # ) 5 ! $ & 89 : ; � � < = > = 2 ? @ A B A C �D E F G E H I J J I K H I L M N O K P Q R S S L T U V W X L M X M L Y M Z Q [ \ ] ] \ ^ [ \ _ ` a \ _ b
c d e e f g h i f j k e l d d mn o p q r s s r n q r t u s v w x u s v w y q p q z t t y q z { z s | } ~2. Marisol solved 60 – 2. What numbers complete the number bond to show how she
used “take from 10”?
60 – 2 = 58
a. 50, 10 b. 60, 0 c. 54, 6 d. 58, 2
3. Carla has 70 paper clips. She gives 6 away. Write a number sentence that shows
how many Carla has left?
_____ - _____ = _____
4. Isaac has 61 pencils. He gives 8 pencils to a friend. How many pencils does Isaac
have left? Draw a picture and write a number sentence to show how you know.
5. Use drawings to explain how to find 31 – 8 and 43 – 8.
___ ___
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� � � � � � � � ! " # $ % # & ! ' # & ( ) ' * + " ' , * # $ + ' ! - . / ! - & ( ) ' * + " ' 0 - 1 . 0 ' / 0 - 2 3 3 + - 4+ % % 5 6 ' # # - ! 7 & ' ! % . # * 4 % * # ) 5 ! $ & 89 : ; � � < = > = 2 ? @ A B A C �D E F G E H I J J I K H I L M N O K P Q R S S L T U V W X L M X M L Y M Z Q [ \ ] ] \ ^ [ \ _ ` a \ _ b
c d e e f g h � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �Name Date
Solve the following 4 problems. Show your number bonds. Draw if that will help you.
1. 20 – 8 = _______ 2. 60 – 5 = ______
3. 21 – 8 = ______ 4. 62 – 5 = ______
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End of Module
Assessment
35
� � � � � �� � ¡ � ¢ ¡ £ � ¤ ¥ � ¦ � � � � � § � � ¨ © ª � «¬ ® ¯ ° ± ± ° ¬ ¯ ° ² ³ ± ´ µ ¶ ³ ± ´ µ · ¯ ® ¯ ¸ ² ² · ¯ ¸ ¹ ¸ ± º » ¼
½ ¾ ¿ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Î Ï Ð Ï Ê Ñ Ï È Ò Ó Ô ÕÖ × Ø Â Ä Ù Ú Û Ú Ü Ý Þ ß à ß Þá â ã ä â å æ ç ç æ è å æ é ê ë ì è í î ï ð ð é ñ ò ó ô õ é ê õ ê é ö ê ÷ î ø ù ú ú ù û ø ù ü ý þ ù ü ÿ
� � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � ! � � � � � � � � � � � � � � � � � � � � �� � � � ! � � � � � � � � � � � � � � � � � � � � � � �� � " � � # � $ � % � & $ � # � & � � � � � � � � � � � $ $ � ' � � ( � � � � � # � � � � � � � ) � � � � � � � � � � � $ � �� � " � � � � � � � � � # � � � � � � ) � �
� � � � � � � ( � �
36
* + , , - ./ 0 1 2 3 4 5 6 7 8 7 0 9 3 : : 3 ; 9 3 4 0 < . = > - ? > @ - = A B + C , , + , , D + . E F G , HI J K L M N N M I L M O P N Q R S P N Q R T L K L U O O T L U V U N W X ¼
½ ¾ ¿ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Î Ï Ð Ï Ê Ñ Ï È Ò Ó Ô ÕÖ × Ø Â Ä Ù Ú Û Ú Ü Ý Þ ß à ß Yá â ã ä â å æ ç ç æ è å æ é ê ë ì è í î ï ð ð é ñ ò ó ô õ é ê õ ê é ö ê ÷ î ø ù ú ú ù û ø ù ü ý þ ù ü ÿ
� � � ! � � ( � �� � Z [ \ ] ^ [ _ ` a ^ a b c ] \ d e a f ` g e h i \ [ ` g ^ ` g c [ g d e ` h ^ j j \ h g e ^ k l m \ [ \ h \ e ] \ n � � � � � � � � � � � # � ' �� �
" � � $ � # � & o � � � � & � � � � � � � � � � � $ � � $ � � � ' � � � � � � p � ) � � � � � � $ �
� � q � � � � � � � ! � � � � � � � � # % ) � � � $ � ' � � r � $ � � � ' � � � � � � # � � � q � � � � � � ) � � � $ s
� �
� � � � � � � � � � � � � � � � � $ & q � � � � � p � ) � s
37
* + , , - ./ 0 1 2 3 4 5 6 7 8 7 0 9 3 : : 3 ; 9 3 4 0 < . = > - ? > @ - = A B + C , , + , , D + . E F G , HI J K L M N N M I L M O P N Q R S P N Q R T L K L U O O T L U V U N W X ¼
½ ¾ ¿ À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Î Ï Ð Ï Ê Ñ Ï È Ò Ó Ô ÕÖ × Ø Â Ä Ù Ú Û Ú Ü Ý Þ ß à ß tá â ã ä â å æ ç ç æ è å æ é ê ë ì è í î ï ð ð é ñ ò ó ô õ é ê õ ê é ö ê ÷ î ø ù ú ú ù û ø ù ü ý þ ù ü ÿ
� � u � v � � � � � � � � � # � � � � � � � ' � � � � � � � � � � � � � � � p � � � � � � � � � # � � � � � � � � � � � � � � # � � � � � � � � %� ! � � � � � � � � � � � � � # � � � � � �� � " � � $ � # � & o � � � � & � � � � � � � � � � # � � � � $ � � � ' � � � � � � � � � � � � � � � # � � � � � � � � � � � �� � � � � � � � �� � � � % � � � � � # � � � � � & u � v � � � � � � � � � # � � � ! � � � � � � � � � � # � � � � � � � � � # � � � � � � � � " � �$ � # � & o � � � � & � � � � � � � � � � � $ � � $ � � � ' � � � ' � � � � � � � ) � � � � � � � # � � � � � � � � � � � �
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