Grade 2 Worksheets

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Second Grade Students in Mathematics. How to Use these Materials with Your Child. Correlation of the Problems with the NGSSS. SECTION 2: Worksheets for ...
Prepared by the University of South Florida Saint Petersburg For a copy of these materials, go to www.cdnportfolio.net/smileyfacemath

Acknowledgements These materials were developed during a Problem Solving for Elementary Teachers class at the University of South Florida Saint Petersburg (USFSP) during the spring of 2009. The worksheets were field tested by the teachers in their own classrooms. The project was conceived and directed by Dr. Charles A. (Andy) Reeves. Dr. Reeves previously developed the Superstars, Superstars II, and Sunshine Math packages of supplementary materials for grades K-8. Dr. Reeves is particularly interested in problem solving and in algebraic thinking. The writers and field testers Allison Chester is a 1st grade teacher at Leila G. Davis Elementary School in Pinellas County, Florida. She enjoys having students use mathematics language in their everyday problem solving activities. Janet Castner and Rene Dieter are 2nd grade teachers at the same school. Janet is interested in bridging mathematics and science curriculum ideas into everyday experiences. Rene is interested in having students derive ways to solve problems without explicit teaching. Barbara Gurian is a 2nd grade teacher at Plumb Elementary School in Clearwater, Florida. She helps students think mathematically while using critical thinking and problem solving in their everyday lives.

Technical Assistance Final proofing and editing was provided by Dr. George Roy, Assistant Professor of Mathematics Education at USFSP. Dr. Roy’s educational interests include pre-service teachers’ development of mathematical content knowledge for teaching. Dr. Zafer Unal, Assistant Professor of Early Childhood Education, USFSP, prepared these materials for the internet. Dr. Unal’s interests include technology in teacher education, institutional and program assessment, e-portfolios, parental involvement and classroom management.

CONTENTS SECTION 1: Introductory Materials Overview of the Next Generation Sunshine State Standards (NGSSS) for Second Grade Students in Mathematics How to Use these Materials with Your Child Correlation of the Problems with the NGSSS SECTION 2: Worksheets for Your Child SECTION 3: Answers to the Worksheets, and suggestions on how to help your child solve the problems.

Section 1

Overview of the Next Generation Sunshine State Standards in Mathematics, K-8, adopted by the State Board of Education in September, 2007.

The Florida Board of Education adopted new mathematics standards in 2007. The standards were developed by Florida teachers, supervisors, and university faculty. The main goal was to reduce the number of standards listed each year so that teachers could focus on fewer topics, but teach those topics in-depth. This emphasis reflects a national trend and our work was based on the National Council of Teachers of Mathematics’ publication Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. (NCTM 2006) The total number of mathematics standards that a K-8 teacher is responsible for covering has been reduced from an average of 87 per grade level, to 18. So teachers will definitely have more time to teach in an in-depth fashion.

Each grade level has three Big Ideas and each Big Idea has several benchmarks under it, usually three or four. There are also Supporting Ideas for each grade level that round out the curriculum and maintain certain strands—algebraic thinking and problem solving, for example—over a several-year span. This strategy combines an in-depth look at the Big Ideas in a given year, with topics that students should work on every year.

The Big Ideas for Grade 2 are:

BIG IDEA 1: Develop an understanding of base-ten numeration systems and place-value concepts.

BIG IDEA 2: Develop quick recall of addition facts and related subtraction facts and fluency with multi-digit addition and subtraction.

BIG IDEA 3: Develop an understanding of linear measurement and facility in measuring lengths.

This means that 2nd graders are going to spend much of their math time (1) developing solid understandings of place value concepts and our base ten numeration system and, (2) developing quick recall for addition and subtraction facts, as well as fluency with multidigit addition and subtraction, and (3) understanding measurement concepts for the linear measure of objects. The Supporting Ideas for Grade 2 come from the Algebraic Thinking strand, the Measurement strand, the Number and Operations strand, and the Data Analysis strand. From the Algebraic Thinking strand, students will express number relationships with charts, with words, and with drawings. In Measurement, they will learn about perimeter, they will measure actual figures using ―friendly fractions‖ like ½ and ¼, and they will practice telling time and ―elapsed time.‖ In the Number and Operations strand, they will use numbers up through thousands, and they will solve non-routine problems by making a chart or list, and by searching for patterns. In the Data Analysis strand, they will make various types of graphs to display data that they collect in the classroom and at home.

In short, your child will be learning much more about fewer math topics than in the past. This shift in emphasis will produce a curriculum that is much more in-depth about very basic ideas, so that re-teaching in future years will be unnecessary. What is necessary, however, is that the ideas learned in one year be used and reinforced in later years. Some have said that the math curriculum will go from a ―mile-wide, inch-deep‖ curriculum, to an ―inch-wide, mile deep‖ curriculum. The truth lies somewhere between those two extremes.

Reference National Council of Teachers of Mathematics, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. Reston, VA: 2006.

How to Use these Materials with Your Child The worksheets that follow are designed to be used during the summer prior to a student entering 2nd grade. The worksheets are similar to Florida’s popular Sunshine Math program where students accumulate stars for doing extra problems. The answers and how to help your child, without giving too much help, are in the back of this package. The directions below are written for the individual parent, but can be adapted by schools, churches, or other community groups sponsoring summer camps for youth groups. The worksheets are each two pages in length so that, if copied front-to-back, they will each use one sheet of paper. Do not feel that you have to ―teach‖ these problems to your child. That’s the job of the school system next year. But many times children learn things incidentally, when talking with others. If you simply talk through the problems with your child, perhaps he or she will remember that type of problem when it’s encountered in 2nd grade, and therefore be more successful with it. Give out one worksheet a week during the summer. You might read all the problems with your child the first night, being sure each problem is well understood, without trying to solve the problems. You should ask for any ideas your child has about how to solve the problems. Then he or she will have all week to work on the problems. When the week is up, have a ―help session‖ with your child in which he or she explains how the problems were solved. Help the child understand the problems that were not solved because similar problems will be seen later during the summer and all next school year. Each problem is worth 1-4 smileys, depending on how hard it is. You can give partial credit if the child understood how to proceed but made a mistake, and you can give a single smiley if the problem was tried but completely missed, assuming the child now understands the problem.

Your child’s reward for doing this extra work is accumulating smiley faces on a chart—you’ll need to make one of those and keep up with it each week. The chart needs to occupy a prominent place in your house, where the child and others will see it regularly. You might consider adding some extra incentives for reaching certain levels. For example, once 10 smileys are earned, he or she gets a book of their choice. For reaching 25 smileys

he or she might get to go to a movie. For reaching 50 smileys, a trip to the beach or a sleepover with friends might be earned. The basic idea is that your child can earn enjoyable rewards by doing some extra math problems. He or she will also realize that next year’s math class will become much easier by knowing how to complete these tasks

SMILEY FACE MATH Markus has this many smiley faces:☻☻☻☺☺☺☺☺☺ Key: ☻ = 10☺

Note: The process of making the smiley face chart is a math task in itself, one from which the child can learn. You—or your child—can make a chart easily using a word processing program by going to the ―insert symbol‖ menu on a PC, and finding the smiley face symbol. As the number of smileys on the chart becomes large, you can use a key such as ☻ = 10☺’s and your child will have learned something else about mathematics—how to construct a useful chart to display data.

Students can use a variety of materials to help them solve the problems. Materials include: Manipulatives to count (beans, chips, tiles, coins) Clocks Money (dollars, half dollars, quarters, dimes, nickels, pennies) Pattern blocks Rulers

Correlation of the Problems and the Next Generation Sunshine State Standards in Mathematics for Second Grade BIG IDEA 1: Develop an understanding of base-ten numeration systems and place-value concepts. BENCHMARK CODE

BENCHMARK

MA.2.A.1.1

Identify relationships between the digits and their place values through the thousands, including counting by tens and hundreds. [ I 1; X 1]

MA.2.A.1.2

Identify and name numbers through thousands in terms of place value and apply this knowledge to expanded notation. [ I 6; X 1; X 6]

MA.2.A.1.3

Compare and order multi-digit numbers through the thousands. 1, 5; XI 9]

[ IV 4, 5; V 8; VIII

BIG IDEA 2: Develop quick recall of addition facts and related subtraction facts and fluency with multi-digit addition and subtraction. BENCHMARK CODE

BENCHMARK

MA.2.A.2.1

Recall basic addition and related subtraction facts.

[VII 4, 8; X 3]

MA.2.A.2.2

Add and subtract multi-digit whole numbers through three digits with fluency by using a variety of strategies, including invented and standard algorithms and explanations of those procedures. [III 5; V 5; VI, 2, 7; VIII 8, 9; IX 7]

MA.2.A.2.3

Estimate solutions to multi-digit addition and subtraction problems, through three digits. [ I 7; VIII 7]

MA.2.A.2.4

Solve addition and subtraction problems that involve measurement and geometry. [III 8; IV 6, 8; V 1, 2; XI 8; VII 8; X 2]

BIG IDEA 3: Develop an understanding of linear measurement and facility in measuring lengths. BENCHMARK CODE

BENCHMARK

MA.2.G.3.1

Estimate and use standard units, including inches and centimeters, to partition and measure lengths of objects. [III 6; IV 8; V 8; IX 6; X 2]

MA.2.G.3.2

Describe the inverse relationship between the size of a unit and number of units needed to measure a given object. [III 6; VI 3, 6; IX 3]

MA.2.G.3.3

Apply the Transitive Property when comparing lengths of objects.

MA.2.G.3.4

Estimate, select an appropriate tool, measure, and/or compute lengths to solve problems. [ IV 8, V 8; VI 6, 8]

[VI 4; IX 3]

Algebra BENCHMARK CODE MA.2.A.4.1

BENCHMARK Extend number patterns to build a foundation for understanding multiples and factors – for example, skip counting by 2’s, 5’s, 10’s. [ I 1, 3; II 1, 5, 6; VII 1, 3, 5, 6; V 3; IX 1]

MA.2.A.4.2

Classify numbers as odd or even and explain why. [III 1; V 6; VII 2; V 7; IX 2]

MA.2.A.4.3

Generalize numeric and non-numeric patterns using words and tables. [ I 1; II 5; IV 1; V 4; VII 3]

MA.2.A.4.4

Describe and apply equality to solve problems, such as in balancing situations. [ II 2, 4; VI 1; VII 8; IX 3, X 7, 8]

MA.2.A.4.5

Recognize and state rules for functions that use addition and subtraction. [ II 5, 6; IV 9; V 4; VII 7]

Geometry and Measurement BENCHMARK CODE

BENCHMARK

MA.2.G.5.1

Use geometric models to demonstrate the relationships between wholes and their parts as a foundation to fractions. [ I 5; V 3; VIII 6; IX 8, X 3]

MA.2.G.5.2

Identify time to the nearest hour and half hour.

MA.2.G.5.3

Identify, combine, and compare values of money in cents up to $1 and in dollars up to $100, working with a single unit of currency.

[ I 2; IV 2, 3; VIII 3; X 5]

[ I 4; II 3; IV 4; V, 6; VII 5;VIII 2; IX 4, 5] MA.2.G.5.4

Measure weight/mass and capacity/volume of objects. Include the use of the appropriate unit of measure and their abbreviations including cups, pints, quarts, gallons, ounces (oz), pounds (lbs), grams (g), kilograms (kg), milliliters (mL) and liters (L). [ I 8; III 8; VI 5; IX 3] Number and Operations

BENCHMARK CODE MA.2.A.6.1

BENCHMARK Solve problems that involve repeated addition. [ I 3; II 3; III 2, 3, 8; VII 5; IX 1; X 4]

Section 2

Smiley Face Math Grade 2, Worksheet I ☺

Name____________________

1. Complete the two patterns. 448, 458, 468, _____, _____, 498, _____, 518 285, 385, 485, 585, _____, _____, _____, _____,1085

☺☺ 2. Jackson ate a cookie at 1:00. He ate another cookie every 2½ hours. Draw the hands to show when Jackson ate his four cookies. The 1:00 cookie is done for you.

☺☺☺ 3. Mario looked at his sister’s tricycle and counted 3 wheels. If his sister had 5 friends over to play, and each brought her tricycle, how many wheels would there be? Answer: _____

☺☺☺

4. Destiny saved 3 quarters, 3 nickels, and 10 pennies each week from her allowance. How much money will she save in 1 week? ______ How much money will she have saved after six weeks? _____________ Explain your thinking.

☺☺☺

5. In each square, draw lines to show fourths. Draw three different ways to show fourths.

☺☺☺☺ 6.

Shown below is a small square, then 10 small squares, then 100 small squares.

one

ten

hundred

a. How many tens are needed to make 100 small squares? _________ b. How many hundreds are needed to make 1,000 small squares?__________ c. How many tens are needed to make 1,000 small squares? _________ d. How many tens are needed to make 2,000 small squares? ________

☺☺

7. Estimate to the nearest hundred. Jenny has 482 marbles, 216 stickers, and 91 shells. About how many items does Jenny have? About ____________ items Explain how you estimated:

☺☺

8. Use the picture to help you solve the problem.

2 pints

=

1 quart

Circle the set which holds less milk.

or Explain how you know:

Smiley Face Math Grade 2, Worksheet II

☺☺

Name___________________

1. Complete the number patterns. Circle if the pattern is increasing or decreasing and tell the amount. 45, ____, 55, 60, ____, ____, 75

Increasing or Decreasing?

By how much? _______

72, 62, ____, 42, ____, ____, 12

Increasing or decreasing?

By how much? _______

☺☺☺☺ 2. Tell what numbers to use for ?, so both sides of the scale will balance.

?

7+8 a.

+6

? = ___ =

b.

7

9-4

-?

? = ___

=

☺☺☺ 3. Joshua has $21.00. A small pizza costs $4.00 and a six pack of soda costs $2.00. He wants to buy 3 pizzas and 2 six packs of soda. Does he have enough money? _______ Explain your answer:

$4.00

$2.00

☺☺☺ 4. I am thinking of two numbers. *Their sum is 15. *One number is 9 more than the other. What are the two numbers?

Answer: _____ and _____

☺☺☺☺ 5. Hollis wants to put one sticker on each of her baby doll’s hands. She made a chart to keep up with how many stickers she will need for the dolls. Number of dolls Number of hands 1 2 2

4

a. Finish Hollis’ chart for 3, 4, and 5 dolls. b. How many stickers does she need for

3

☺☺

her 5 dolls? ________

4

c. Explain how many stickers Hollis needs

5

for any number of dolls she might have:

6. Complete the pattern. One yard equals 3 feet and two yards equal 6 feet. yards

1

2

3

4

5

6

feet

3

6

___

___

___

___

☺☺☺☺ 7. Compare. Write >, and < as being an open alligator mouth. The gator always wants to eat a number bigger than he is. So his mouth opens toward the bigger number. If the numbers are equal, use =.

a.

882

881

b. 327

327

c.

310

301

d. 123

132

Smiley Face Math Grade 2, Worksheet III

Name____________________



1. Is 11 an even number or an odd number? ________

☺☺

2. Victor earns 5 minutes of center time each day he turns in his homework to his teacher. How much free time will he have earned if he turns in his homework for 11 days? Answer: ______ minutes

How do you know?

☺☺☺ 3. Each piece of candy costs 7 cents. Cori has 50 cents. How many pieces of candy might Cori buy?

7¢ Answer: Cori might buy ______ pieces of candy.

☺☺☺ 4. Alex has $2.50. He wants to buy one of each of the toys. Does he have enough money? _____ How do you know?

$0.65

$1.15

$ 0.40

☺☺

5. Add 48 + 33.

48 +33

How can you use subtraction to check your work?

☺☺☺ 6.

a. Measure the length of the leaf to the nearest inch.

______ inches

b. Measure the length of the leaf to the nearest centimeter. ______ centimeters c. Explain why part (a) has a smaller number than part (b):

☺☺

7.

Janet’s aquarium is the shape of a rectangular prism. It has a glass top. How many faces does it have? _____ How many edges does it have? _____ How many vertices does it have? _____

☺☺☺ 8. Janet’s aquarium holds 40 liters of water. How many times would you have to pour a 2-liter bottle of water into Janet’s empty aquarium, to totally fill it? Answer: _____ times

Smiley Face Math Grade 2, Worksheet IV



Name: _____________________

1. Tell in your own words how to make this pattern: ▲▲►▼▲▲►▼▲▲►▼▲▲►▼ ........ Answer: You make the pattern this way:

☺☺☺ 2. What time will show on the clock in four hours? _______

In 10 hours? ________

☺☺☺ 3. Bella earns a quarter for making her bed every day. At the end of one week, how much money does Bella have? ______________



4. Billy made seventeen baskets in his last game. Danny made fourteen baskets. Who made more baskets, Billy or Danny? ________ How many more baskets? _______



5. Remember the alligator mouth! Show the bigger number of baskets by writing > or < in the box. 17

14

☺☺

6. How many sides do the four rhombi have altogether? Answer: _____ sides

☺☺☺ 7. If the four rhombi above were pushed together, the figure might look like: How many sides does the new figure have? (The sides are the outside edges.) Answer: ____ sides ☺☺☺ 8. If each edge of the rhombus is 2 inches long, what is the perimeter of the shape above? Remember the perimeter is the length around the outside edge. Answer: The perimeter is _____ inches.

☺☺☺ 9. Study the “in and out” table. Find and tell the rule of how to start with an in number, and get the out number What is the rule? _______________________________________________________ Use the rule to complete the table. IN

OUT

10

20

5

15

7

17

1

11

14 8 55

10 in

What am I doing to numbers? out

20

Smiley Face Math Grade 2, Worksheet V 

Name: _____________________

1. Marcus wants to build a rectangular fence for his dog Marley. Two sides will be 20 feet long and two sides will be 15 feet long. How many feet of fence does he need to buy? Answer: He needs to buy ___ feet of fence.



2. Marcus wants to put a pole every 5 feet to hold up the fence. How many poles does he need to buy? Answer: He needs to buy ___ poles.



3. How many triangles like the one below fit into the hexagon? ____ the hexagon is the triangle? Answer: ____



4. Think about the second row of numbers in the chart. What are the 7th and 8th numbers in the second row? Answer: ____ and ____ 1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

12

15

18

21

24

27

?

?

36

39

Tell in words how you know:

What fraction of



5. Al has 642 baseball cards. His brother Toby has 128 less than Al. How many baseball cards does Toby have?

_______ baseball cards



6. Chelsea had two $1 bills and a quarter to spend at the candy store. Her sister Ashley had 8 quarters, 3 dimes, and a nickel. Which sister had more money to spend? _______ How much more? ________

Chelsea-

Ashley-



7. There are 13 crayons in the package below. Is 13 an even or an odd number? Explain how you know. Answer:



8. Make a paper airplane. Throw it and measure how far it goes in inches. Answer: ___ inches Throw it a second time and measure how far it goes this time.

Which throw went the longest distance?_________ How much longer was it? ________inches longer

Answer: ____ inches

Smiley Face Math Grade 2, Worksheet VI

Name: _____________________

☺☺☺ 1. Each apple below weighs 12 ounces. Jorge made 4 bananas balance with 3 apples. How much does each banana weigh? _______ ounces

☺☺

2. What number is shown by the blocks below?

_______

How many blocks would there be if you added 29 more blocks? _______ blocks

How many blocks would be left if you removed 25 from the original group? _______ blocks

☺☺

3. Rose wants to measure her bedroom. She can’t decide between using a ruler or a yardstick. Which tool would she have to put down more times, the ruler or the yardstick, to measure the room? ______________ yardstick

ruler

Explain why:

☺☺☺☺ 4. If 4 cups equal a quart, how many cups are in 3 quarts?

=

so _____ cups = 3 quarts

☺☺☺ 5. Draw and label 3 pencils, A, B, and C, so that: Pencil A is longer than pencil B, and Pencil B is longer than pencil C. Is pencil A longer or shorter than pencil C?

Answer: ______________________________________________

☺☺☺ 6. Circle the unit of measure you would use to weigh a full back pack.

☺☺

a. pounds

b. quarts

c. liters

d. meters

7. Jonah had an ant farm with 234 ants. His little brother’s ant farm had 169 ants. How many more ants did Jonah’s ant farm have?

_________ants

☺☺☺ 8. Without measuring, how tall do you think you are? Circle 3, 4, or 5 feet. a. After measuring yourself, about how tall are you? Answer: I’m about ____ feet tall. b. Find one thing in your house taller than you. Estimate its height, using your height: Answer: ___feet c. Find one thing in your house shorter than you. Estimate its height, using your height: Answer: ___ feet

Smiley Face Math Grade 2, Worksheet VII ☺☺☺☺ 1.

Name: _____________________

Use this hundreds chart. a. Write in the missing numbers. b. Skip count by 2s and color the numbers you counted light green. c. Skip count by 5s and color the numbers you counted light red. d. Draw a circle around any numbers that are colored both red and green.



2. Look at the numbers you colored light green in the hundreds chart above. These numbers are all even numbers. Numbers that are not colored light green are odd numbers. How can you tell an even number by looking at the ones digit? Answer: An even number ends in ____, ____, ____, ___, or ____. How can you tell an odd number by looking at the ones digit? Answer: An odd number ends in ____, ____, ____, ___, or ____.

☺☺

3. Add the next five symbols to the pattern below:

Z, Y, 1, Z, Y, 2, Z, Y, 3, Z,

_____, _____, _____, _____, _____

Explain how to make the pattern:

☺☺

4. Kylie has six bags of marbles. There are five marbles in each bag. How many marbles does Kylie have? ______ marbles

☺☺☺ 5. Use one of these symbols to compare the value of these coins.

less than < greater than > the same as =



Use the symbol here

6. What is the total number of sides for five triangles? ________ sides

☺☺☺ 7. Look at the “input-output” table. What is the rule? Complete the table. INPUT

OUTPUT

6

4

9

7

4

2

Rule: For each input number, I

to get the output number.

8



8. Rita put 14 blocks on the right side of a balance scale. She put 8 blocks on the left side. Help her add enough blocks to make both sides equal.

8 + ___

=

10 + 4

Smiley Face Math Grade 2, Worksheet VIII



Name: _____________________

1. The baseball team has shirts with these numbers: 36, 19, 45, and 32. Write the numbers on the shirts from least to the greatest.

least number

☺☺

greatest number

2. John wanted to buy a toy that cost $0.68. He had one quarter, two dimes, and a penny. Did John have enough money to buy the toy if there was no tax? Circle yes or no.

$0.68 How do you know?

☺☺

3. This is the time Abby’s alarm goes off in the mornings. Abby’s school begins one and a half hours later. What time does Abby start school: _________a.m.

☺☺☺ 4. If you counted six kids ahead of you in line for the bus, then counted seven kids behind you, how many kids were in line for the bus? _____ kids



5. Put the numbers below in order from least to greatest.

574, 253, 123, 547, 808, 828 __________, __________, __________, __________, __________, __________

☺☺☺ 6. Use this pizza to show some fractions. Each slice is one-eighth (1/8) of the pizza. Mark ate 4 slices. What fraction for the pizza did he eat? _____ of the pizza Sally ate 3 slices. What fraction of the pizza did she eat? _____ of the pizza After Sally and Mark ate, the dog got what was left over. What fraction of the pizza did the dog eat? _____ of the pizza



7. Estimate, by rounding to the nearest hundred, the sum of :

321, 487, and 102

Answer: My estimate is _______.

☺☺

8. Give an exact answer. Find the sum of the numbers in problem 7:

☺☺

9. Subtract to find out how far off of the exact answer your estimate was in problems 7 and 8.

_________

Answer: My estimate was _________ away from the exact answer.

Smiley Face Math Grade 2, Worksheet IX

☺☺☺ 1. Four children are playing in the water. How many toes are playing in the water?

Name: _____________________

_________ toes

Show your work. Explain with pictures, words, or numbers.

☺☺

2. Sarah rolled two dice. She rolled a three and a six. Was the sum of the two dice even or odd? ________ How do you know?

☺☺☺☺ 3. How much weight does it take to balance 4 plastic oranges? Write the weight inside the box below.

10 g

____

5g

g



4.

Tommy has 3 quarters, 2 dimes, and 1 penny in his piggy bank. How much money does he have? _________ ¢

☺☺

5. Can Tommy buy an ice cream cone for himself and one for his mom? ___________ Explain:

Ice cream cone

35¢ ☺☺

6. How long is the tape holder below?

_____ centimeters

Thao said the tape holder was 25 centimeters long. Explain what was Thao doing wrong.

☺☺☺ 7. Write digits in the boxes below so the problems will be correct.

a. 32 +3 5 357 ☺☺

b. $7. 6 –.4 5 $6.9 1

c. 3, 4 7 5 +1 1__ 3, 5 8 9

8. One piece of pizza costs 75 cents. There are six slices in each pizza. (a) How much would it cost to buy the whole pizza?

________

(b) If Sam ate 2 pieces, what fraction of the pizza did he eat? _____

Smiley Face Math Grade 2, Worksheet X ☺

Name: _____________________

1. Becky and Ben were counting their $100 bills in a game of Monopoly. ... eight hundred; nine hundred; one thousand, one thousand, one hundred; one thousand, two hundred. That’s all my money.

... eight hundred; nine hundred; ten hundred; eleven hundred; twelve hundred. That’s all my money.

Who had the most money, or did they have the same amount? Tell how you know.

☺☺☺☺ 2. Take out 3 regular sheets of notebook paper. Each piece of paper is 8½ by 11 inches. Estimate how many inches the perimeter is for one sheet of paper. (The perimeter is how far it is around the outside edge.) _____ inches

Now lay the 3 sheets down beside each other, with 11-inch sides touching. What is the perimeter of the 3 sheets of paper? ____ inches

☺☺☺ 3. Take one of your sheets of notebook paper and fold it down the middle. Now turn it the other way and fold it down the middle again. It should look like this

Color in 3 of the pieces. What fraction of the sheet of paper is colored? _____

☺☺

4. One orange weighs 8 ounces. How much will a. b.

4 oranges weigh? __________ 7 oranges weigh? ______

☺☺

5. On the left, draw the hands on the clock to show 10:30. On the right, draw hands to show 3 hours after 10:30.

☺☺☺ 6. Look at the number in the calculator’s display window.

Which digit is in the ones place? ____ Which digit is in the tens place? ____ Which digit is in the hundreds place? ____ Which digit is in the thousands place? ____

☺☺

7. Two cylinders balance 3 cubes. How many cubes will balance with 6 cylinders?

?

☺☺☺ 8. In the problem above, if a cylinder weighs 15 grams, how much does a cube weigh? Answer: ____ grams Explain how you know:

______

Section 3

Suggestions for helping your child find the answers Grade 2, Worksheet I

1. Answers: a. 478, 488, 508; b. 685, 785, 885, 985 Your child will first need to recognize whether the numbers in each pattern are increasing or decreasing. The numbers in the first pattern are increasing by 10. The numbers in the second pattern are increasing by 100. Children may have difficulty reading 1,085. They may not have encountered numbers in the thousands in school yet. You may want to explain that ten hundreds equal one thousand, which comes up in problem 6. 2. Answer: 1:00, 3:30, 6:00, 8:30 If you have a clock with movable hands, you can have the child count forward from one o’clock 2½ hours. They can tell the hour by looking at where the short hand is pointed, or where it recently passed. The long hand points at the minutes. They can find the minutes by counting forward individual marks starting at 12, or they may ―count by fives‖ for each number past 12. You may want to point out that anytime it is half past an hour (:30), the minute hand is always pointing at the 6 and the hour hand is always exactly in the middle between two numbers. When the time is exactly on the hour (:00), the minute hand is always pointing to the 12 and the hour hand is always pointed directly at a number, indicating that hour. 3. Answer: 18 wheels Ask the child if he or she should count Mario’s sister, which they should do. So that’s 6 children total, each with a tricycle. The child can put out 3 counters for each of the six children or draw such a picture. Encourage them to ―count by 3s‖ to find the answer. They can say intermediate numbers quietly but emphasize the multiples of three, as in ―1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18‖. Or the child might just say ―3, 6, 9, 12, 15, 18.‖ 4. Answer: $1, $6 Your child may not have encountered counting change to a dollar. If you have coins, allow your child to use them to count the amount given in the problem. After identifying the amount saved for one week ($1.00), your child may need prompting to think about the other five weeks in which Destiny also saved $1.00. Think: $1.00 + $1.00 + $1.00 + $1.00 + $1.00 + $1.00 = $6.00. 5. Answer: will vary Any of the following divide the square into fourths, as do other shapes. The main point is for the child to show 4 equal parts of each square.

6. Answer: 10, 10, 100, 200 With limited exposure to numbers in the thousands, your child might draw a picture or use cut-outs of the tens and hundreds shown to solve this problem. They may even use a separate piece of paper since a drawing will take up much space. There are 10 hundreds in each thousand. Your child may be able to

recognize that 10 hundreds taken 2 times is 20 hundreds or 2,000. There are 10 tens in each hundred; there are 100 tens in each thousand. One hundred tens counted twice is 200 tens or 2000 small squares. 7. Answer: 800 items The purpose of this question is to have the child round each of the three numbers to the nearest hundred. 482 is closest to 500. 216 is closest to 200. 91 is closest to 100. The child then adds 500 + 200 + 100 = 800. You might point out that sometimes we don’t need to know an exact answer—the purpose of an estimate is to help develop ―number sense.‖ ―Explain your answer‖ and ―How do you know‖ encourage children to review and monitor their thought process. 8. Answer: 5 pints is less than 3 quarts This problem introduces your child to capacity of pints and quarts and how they are related to one another. If you have pint and quart containers at home, use them to demonstrate their capacity. If your child is ready for a discussion on fractions, you might mention that 5 pints would be the same as 2½ quarts, and show them how to write that number.

Suggestions for helping your child find the answers Grade 2, Worksheet II 1. Answer: a. 50, 65, 70; Increasing by 5; b. 52, 32, 22; Decreasing by 10. The purpose of this problem is to have the child identify the patterns, and to determine whether the numbers in the pattern are increasing or decreasing in value, and by how much. If your child doesn’t recognize the pattern by seeing it visually, have them say the numbers out loud, in order— sometimes the verbal reinforcement will make the pattern more obvious. 2. Answer: a. 9; b. 2. Your child may not have experience with balancing an equation. When going over the problem with the child, be sure to use the Hint to help. You might take out a pencil or ruler and balance it on one finger, and show them that anything put on one side has to be the same as something put on the other side, for it to balance. 3. Answer: Yes, Joshua has enough money. 3 pizzas cost $12.00 and 2 six packs of soda costs $4.00. Joshua only needs $16.00. Your child may like to use dollar bills or may choose to draw a picture to solve this problem. 4. Answer: 12 and 3. Children will have to remember that sum means the answer to an addition problem. Therefore, the two numbers will have to be added together to equal 15. Making a chart of the various combinations would be helpful. For example, 1 and 14, 2 and 13, and so on, all add to 15. The child will have to figure out which two numbers meet the criteria “One number is 9 more than the other.” Children may also guess, check, and revise. 5. Answer: a. 6, 8, 10 hands; b. 10 stickers c. she could double the number of dolls, or add the number of dolls to itself, to get the number of hands. The purpose of this problem is to have the child complete a chart by counting or by identifying a pattern. The number of hands also represents the number of stickers needed per doll. Later, this will become a multiplication problem; 5 × 2 = 10. For now, the child might ―act it out‖ if they are having difficulty understanding what the problem calls for. Question c is there to evoke a generalization on the child’s part—they probably won’t know what the question means. First talk to the child about different numbers of dolls she might have—10, 15, and so forth. Then ask if there’s a way to tell someone else how to find the number of hands, if you know the number of dolls. 6. Answer: 9, 12, 15, 18 to complete the chart; 18. The purpose of the problem is for children to recognize the pattern and complete the chart. Children may simply count by 3s or may draw a picture using sets, tally marks, or some other illustration to solve it. This problem should further develop the relationship of yards to feet. 7. Answer: See below. Be sure to discuss with the child the ―alligator mouth‖ way to remember which number is greater. Ask them to explain how they decided each symbol. a. b. c. d.

882 (>) is greater than 881 327 (=) is equal to 327 310 (>) is greater than 301 123 (. This problem returns to last week’s problem about using the symbols < (less than) and > (greater than). Ask your child if they remember about the alligator’s mouth, and what that picture means. 6. Answer: 16 sides Have your child trace around the edge of each rhombus, and when they change direction, count one more. Or they might mark each edge as they go, to keep from counting sides over again. Some children will immediately say 4, 8, 12, 16—the group has 16 sides. They will be adding 4’s repeatedly, or counting by 4, a precursor to multiplication. 7. Answer: 4 sides. This question will be difficult for some children as they will want to count the interior lines of the figure, just as they did above. However, when shapes are joined together to create new shapes, sometimes edges that were previously sides become interior features, and so aren’t sides of the new shape. Tell your child that the side of a figure is just the outside edge. 8. 20 inches. You might ask your child if they know what perimeter means—it’s the distance around the outside of a polygon. He or she can practice counting by 2s around the edge of the shape, marking off the pieces as they go.

9. Answer: Rule: add 10 to the input; 24, 18, and 65 go in the chart. By looking at the table, the child should discover the pattern of adding 10. If they don’t, take the input and output pairs one at a time, being sure they know what ―input‖ and ―output‖ mean. Use the picture of a function machine to help them visualize these terms. Then give them some other input numbers and see if they can tell you the output. Once they see this pattern, he or she should be able to finish the chart.

Suggestions for helping your child find the answers Grade 2, Worksheet V 1. Answer: 70 feet Suggest that your child draw a picture of the rectangle, looking down from above, and label the length of the sides as shown below. Then they can see that the total length, or perimeter, is 20 + 20 + 15 + 15 or 70 feet. 15 20 2. Answer: 14 poles Again suggest a ―top down‖ drawing like the one above, but put in poles every 5 feet. The child can then count the poles.

3 Answer: 6 triangles, 1/6 You can have your child draw the triangles in the hexagon to determine the number of triangles that would fit inside it. You may also wish to use pattern blocks. The fraction is 1/6 because the triangle is one of 6 equal parts that make the hexagon.

4. Answer: 30, 33; The pattern is increasing by 3 so the 7th number is 30. By looking at the pattern from left to right, the child can probably determine that it increases by three each step. If not, have them say the numbers out loud and put down that number of counters for each new cell. The seventh number would be found by adding three to the 6th number in the table. You would do the same to determine the eighth number. 1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

12

15

18

21

24

27

30

33

36

39

5. Answer: 514 baseball cards. This word problem asks the child to find out how many baseball cards Toby has. The child only knows that Al has 642 and Toby has 128 less than Al. This might be difficult for your child to determine what he/she needs to do to

solve the problem of comparing numbers. Once the child determines that they need to subtract to find out Toby’s amount, they can set up the problem. 642 – 128 = 514 If your child hasn’t done subtraction problems where regrouping—borrowing—is required, you can show them how with drawings of base ten materials. Or you can let them use a calculator. 6. Answer: Ashley, 10¢ more Your child might add up the amount of money for each girl and compare, then subtract Chelsea’s amount from Ashley’s amount. Chelsea has $2.25 and Ashley has $2.35. Therefore, Chelsea has 10¢ more to spend. You may wish to give your child money to help them count the coins. Or, if they know that $1 = 4 quarters, he or she can mark out $1 for Chelsea and 4 quarters for Ashley, two times, leaving Chelsea’s quarter compared to Ashley’s 3 dimes and a nickel. Since a quarter equals two dimes and a nickel, you can mark out those two amounts, leaving Ashley with a dime as the only unmarked coin.

Chelsea-

Ashley-

7. Answer: odd; I know it is odd because if I try to pair up 13 crayons, 1 of the crayons won’t have a match. Have the child use 13 counters or draw 13 crayons and try to match them up. If there are no crayons left without a match, it is an even number. Use this opportunity to look for ―partners‖ that make even numbers. Remind them of doing this on Worksheet III two weeks before. Give them some other numbers of objects, to see if they can determine even or odd. 8. Answers: will vary Help your child make a paper airplane, and you make one too. Have them measure their airplane’s flight several times before doing the problem. You’ll have to pick a starting line, and then measure on a straight line from the starting line to the nose of where the plane lands—don’t try to measure its twists and turns. Rounding will also be involved. The purpose is for the child to practice measuring in inches, and also practice subtracting with several digits involved. If the child doesn’t know how to regroup for subtraction, have them estimate and then allow them to use a calculator.

Suggestions for helping your child find the answers Grade 2, Worksheet VI 1. Answer: 9 ounces

12

12

12

=

9

9

9

9

The main point of this problem is to introduce the concept of equality, a concept central to algebraic thinking. If you have apples and bananas at home, you might show them visually what this would look like. Ask them how much weight, total, are the apples (36 ounces). Then ask—if 4 bananas have to be the same weight, how much would each banana weigh? The child may not know to divide, so they can guess different weights for the bananas until they find a weight—9 ounces—for which 4 of them gives 36 ounces. This problem is a beginning to algebraic thinking and solving equations. 2. Answer: 42, 71, and 17 Children can count the blocks. They should know that the rod is equal to 10. Count by 10’s then add two more to get 42. They can draw more rods and blocks beside those pictured to show adding 29 more. The difficult part will be to regroup 2 single blocks and 9 single blocks to give another rod and 1 block, giving 71 in the end. Similarly, they can go back to the original group and remove 2 rods and 5 single blocks, but then need to regroup the 4 rods and 2 blocks to 3 rods and 12 blocks before beginning. 3. Answer: She will use fewer yardsticks than rulers. A yard is equal to 3 feet. A ruler is equal to 1 foot. If you have a ruler or yardstick at home, practice measuring a side of a room to see the difference. The important part is for the child to understand the inverse relationship at work. It takes fewer repetitions of a larger unit to go a certain length, than of a smaller unit. 4. Answer: 12 cups Use a measuring cup and have the child fill it four times with water, calling it 1 quart. Then repeat that action 2 more times, getting 12 cups when they say ―that’s 3 gallons.‖ If you don’t have a measuring cup handy, the child can draw a picture to show that 12 cups would equal three gallons. 5. Answer: Pencil A is longer than pencil C. If your child has difficulty understanding what they are to do, take 3 pencils of obviously different lengths, and go through the statements comparing length. Have the child draw their own conclusion, with you simply asking leading questions. (If you don’t have pencils handy, substitute another such length model or have the child draw a diagram of the pencils.)

6. Answer: pounds Discuss with your child that we have different ways to measure weight, height, volume, etc. It’s important for them to learn which of the standard measures is called for in measuring something. If someone asked how tall they are, for example, it wouldn’t tell them anything to say ―I weigh 43 pounds.‖ If the child has a backpack at home, fill it with books and use the family scale to see how much it actually might weigh. 7. Answer: 65 more ants Your child should be able to set up the subtraction problem as 234-169. This might be your child’s first exposure to regrouping or ―borrowing.‖ If so, and you don’t have manipulatives to show them, allow them to use a calculator to solve the problem. For a nice way to practice using manipulatives on a computer, go to http://nlvm.usu.edu/en/nav/frames_asid_155_g_1_t_1.html?from=category_g_1_t_1.html. 8. Answer: will vary The important point of this problem is for the child to estimate their own height in feet, and then use their height to estimate other heights. This teaches the child to use common sense and benchmarks when measuring items, which is a valuable skill for use in everyday life. Talk through the parts of this problem, and then go with them through the house, observing as they proceed.

Suggestions for helping your child find the answers Grade 2, Worksheet VII 1. Answers: See bold numbers. Colored light green would be the columns under 2, 4, 6, 8 and 10; colored light red would be the columns under 5 and 10; colored both green and red would be the 10s column. This problem provides a chance for your child to practice counting by 2s and by 5s. If they have trouble, have them count by 2s by pointing first to 2, then skip a number and move their finger to 4, and so on. The verbal and kinesthetic reinforcement should help them learn to count by 2s. Similarly for counting by 5s. Be sure to discuss with them the visual pattern that emerges, with columns all one color. . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

22

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31 41

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33 43

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36 46

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54 55 64 65

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76 86

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79 89

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42

87

2. Answer: An even number ends in 2, 4, 6, 8, or 0. An odd number ends in 1, 3, 5, 7, or 9. Previously the difference between even and odd numbers was approached as ―even numbers of objects can always be paired up, with none left over. Odd numbers always have one object left unmatched, when you try to pair them up.‖ This method works for small numbers, but as numbers get larger, you want students to notice that they can also tell even from odd by looking at the ones digit. 3. Answer: Y, 4, Z, Y, 5; the pattern has Z and Y repeating, but the numbers after each Y go up by 1 every time through If your child has trouble seeing the pattern, have them point to the first letter, Z, on the left, then say each new term as they point to it, moving to the right. Z restarts the pattern. 4. Answer: 30 marbles. Your child might need to use manipulatives or draw a picture to show the 6 bags, with 5 marbles in each bag. This problem is an introduction to repeated addition by 5, and could also be solved by 5 + 5 + 5 + 5 + 5 + 5 = 30. Or the child might simply count by 5s, going 5, 10, 15, 20, 25, 30. This type of problem is the beginning of understanding multiplication as six groups of 5, or 6 × 5 = 30.

5. Answer: > since 3 quarters is 75¢, which is greater than 6 dimes or 60¢. You may wish to give your child coins to help them count the change. Remind them to make the symbols for less than and greater than look like an alligator’s mouth wide open. The gator always wants to eat the greater number. 6. Answer: 15 sides. Encourage your child to use repeated addition to solve the problem, 3 + 3 + 3 + 3 + 3 = 15. Or, they might simply count by 3s—3, 6, 9, 12, 15. Some might even realize that 3 × 5 = 15. 7. Answer: Rule: subtract 2; the missing number is 6. You might need to remind your child of what an ―input-output‖ machine does. It is set to do the same thing to any number that goes into the input. The child needs to look at several input-output pairs together, to see what the machine seems to be doing. In this case, if 6 goes in, 4 comes out; if 9 goes in, 7 comes out; if 4 goes in, 2 comes out. If this is not enough information for the child, then give them some more input-output pairs. A visual example like the one below might help. This child constructed a ―+10‖ input-output machine.

8. Answer: 8 + 6 = 10 + 4 Children have a difficult time understanding what equal means. This balancing situation is a physical embodiment of what equality means in algebra. Suggest that your child draw boxes to equal the same number as on the right. Ask him or her to solve the right side of the problem first, 10 + 4. They know that this equals 14. Therefore, the left side of the problem must equal 14 too. Ask your child what number, plus 8, would equal 14. They might count up to find the answer or subtract 8 from 14.

Suggestions for helping your child find the answers Grade 2, Worksheet VIII 1. Answers: 19, 32, 36, 45. A hundred’s chart or writing numbers on a number line might help students put these numbers in order. Students coming into 2nd grade should be able to read numbers from 1 to 100 and they should realize that the right-most digit tells the ones while the 2nd digit from the right tells the tens. 2. Answer: No. He does not have enough money to buy the ball. He only has 46 cents. If your child has trouble with this problem, use real coins and have the child tell how much each is worth in turn. 3. Answer: 8:30 a.m. If your child had trouble with time, find out if they understand which hand stands for hours. A common mistake is either saying 7:12 or 12:7. Help them by talking about ―o’clock‖. Practice by making a clock and just moving the hour hand. 4. Answer: 14. A common mistake is forgetting to count themselves—the child might simply add 6 and 7 because they see those numbers in the problem. Children should be encouraged to draw a diagram for this problem, then count the marks they made. Bus

xxxxxxYxxxxxxx 6 ahead you 7 behind

5. Answer: 123, 253, 547, 574, 808, 828. Hopefully the child will look at the hundreds column first for placement. If two numbers start with the same they then must go to the tens column and so on. 6. Answers: four-eighths, three-eighths, and one-eighth. Very few children will know how to write these names using numerals, but you might show them to your child. The key idea for them to understand is the last number—eighths—tells how many slices of pizza, all equal, make up the whole pizza. The first number tells the number of those slices being eaten. If using symbols like 4/8, 3/8, and 1/8, the ―bottom number‖ is the denominator; the top number is the numerator. You should not stress these names with your child, but you can mention them in passing. 7. Answer: 900 Discuss with your child what it means to ―round to the nearest hundred.‖ It means to use the hundreds number that’s closest to the number you are considering. Your child might mention ―front end rounding‖ which is popular in schools today—if your child does mention this, then ask them to explain that method to you and how they find answers that way. 8. Answer: 910 If you child has not encountered adding 3-digit numbers in which numbers must be regrouped, then you might allow them to use a calculator. You can easily show how to regroup such numbers if you have base-ten blocks to use. 9. Answer: 10 If your child got problems 7 and 8, this should be easy as they can probably tell you the difference in 900 and 910, just by using mental arithmetic.

Suggestions for helping your child find the answers Grade 2, Worksheet IX 1. Answer: 40. If necessary, suggest that your child draw a picture of the toes and count. This is an example of ―skip counting‖ which is the start of repeated addition and thus multiplication. The child might skip count by 5s, saying 5, 10, 15, etc., up to 40, or skip count by 10s. The child might also add 5 eight times, or add 10 four times. 2. Answer: odd. Your child can use the pictures (top of the dice) to help her or him with this problem. This is also a good time to use manipulatives (pennies, rocks, tiles, etc.) to show 9 counters. Hopefully the child will remember that even numbers, when put in two matched groups, will always come out matched up, with no unmatched counters. Odd numbers, when you try to match them up, always have one leftover counter. 3. Answer: 20 grams. This may be difficult for your child because he or she must first determine how much each orange weighs by adding the left side of the left-hand scale together (10 + 5 = 15). So from the left-hand scale, 3 oranges balance 15 grams, so each orange must be 5 grams. Then look at the balance scale on the right. You could explain how a balance scale is like a see-saw. If each orange weighs 5 grams, how much would 4 oranges weigh? 5+ 5 + 5 + 5 = 20 grams. 4. Answer: 96 cents Encourage your child to use real money. If your child has difficulty counting quarters, teach them a way to skip count by fives. Draw five dots on the quarter and two dots on the dime. Then just skip count by fives. Money will be a major focus in 2nd grade and you’ll want to give your child many opportunities to practice. 5. Answer: Yes

Two of the ice creams would cost 70 cents, so 96 cents is enough.

6. Answer: a. About 21 centimeters b. Thao did not notice that the tape holder was not lined up starting at the left end of the scale, the ―zero‖ point of the scale. Starting on the ―0‖ is an important part of measuring. This problem is a bit tricky for 2nd graders. Your child has to see that the tape dispenser would have to be moved to the zero, or that the measurement is 25 – 4, which is 21. 7. Answers: a. 2 b. 6 c. 4 These puzzles are sometimes difficult for children because we have some unknowns. Base ten hundreds, tens, and ones will help them ―see‖ what is missing. Money could also help on puzzle b.

a. 322 + 35 357

b. $7. 36 - . 45 $ 6 . 91

c. 3, 475 + 114 3,589

8. Answer: a. $4.50 b. 2/6 If your child has difficulty adding 75¢ six times, allow them to use a calculator. Encourage them to explain when this fraction is called ―twosixths‖. What does the ―sixths‖ mean, and what does the ―two‖ mean?

Suggestions for helping your child find the answers Grade 2, Worksheet X 1. Answer: They had the same amount. Read aloud the number names that both Becky and Ben are saying, with your child. Becky is regrouping hundreds when she says ―one thousand‖; Ben is continuing to count hundreds. Both are legitimate ways to count and both ways come up often in the real world. It will help your child to realize that ―eleven hundred‖ is another name for ―one thousand, one hundred‖, and so forth. 2. Answer: 38 to 40 inches; 70 to 76 inches. Be flexible in accepting an answer from your child as they probably don’t know how to add 8½ + 8½ yet. They might add those lengths as 8 inches or nine inches, or intuitively know how to add 8½ itself. The main point of this problem is to review perimeter of a figure, and also that the sides of individual pieces aren’t always sides of a different figure when pieces are joined. The actual perimeter of the single sheet is 11 + 11 + 8½ + 8½ inches, and for the three sheets together is 11 + 11 + 8½ + 8½ + 8½ + 8½ + 8½ + 8½ inches. A meaningful way for the child to check and see how close their answer is, would be to take a yardstick or a carpenter’s tape measure and actually measure the sides, finding the perimeter as the total length measured. 3. Answer: 3/4 Have your child fold such a sheet of paper and go through the coloring activity. You will probably have to ask them how many pieces the whole paper has been partitioned into—that’s where ―fourths‖ comes from—and how many pieces are under consideration. 4. Answer: 32 and 56 The main point of this problem is for the child to skip count, or repeatedly add the same number, which is a foundation for multiplication in 2nd grade. 5. Answer: 10:30 and 1:30 You might have to review with your child that the hour hand is the shorter hand, and for the minute hand, you ―count by 5s‖ as you progress around a clock face. When the minute hand is on 6, the hour hand should be half-way between two numbers to show that ½-hour has passed. 6. Answer: 8, 7, 6, and 5 Have your child explain to you the place value of digits, and how the smaller numbers—the ones—start at the right and get bigger as you move to the left. Note that this is different from the way they learn to read words and sentences. 7. Answer: 9 This problem might confuse your child as they might not know that they have to use the information in one picture, to help complete the second picture. Since two cylinders balance 3 cubes in the scale on the left, ever time you see 2 cylinders, you can replace them, weight-wise, with 3 cubes. So as you mark pairs of cylinders in the scale on the right, you can add 3 cubes to the right-hand pan. 8. Answer: 10 grams Your child can probably do this problem intuitively or through guesscheck-revise, even though they don’t know how to divide yet. The two cylinders on the left would weigh 30 grams together, so 3 cubes would weigh 30 grams. The child can then ask himself or herself—what number can I add three times, and get 30? Ten, of course.