Go through the enVision Math Common Core Grade 2 Answer Key Topic 2 Work with Equal Groups and finish your homework or assignments.

## enVision Math Common Core 2nd Grade Answers Key Topic 2 Work with Equal Groups

Essential Questions:
How can you show even and odd numbers? How do arrays relate to repeated addition?

enVision STEM Project: Plants, Animals, and Arrays
Find Out Make lists of different types of plants and wild animals that you see. Look in your neighborhood or in a nearby park. Look at how the animals and plants come together.
Journal: Make a Book Show what you find out in a book. In your book, also:

• Tell about plants or animals that you see in groups. Look for patterns.
• Make an array of a group of plants and an array of a group of animals.

A number which is divisible by 2 and generates a remainder of 0 is called an even number. An odd number is a number which is not divisible by 2. The remainder in the case of an odd number is always “1”.

The property by which we classify an integer in math as even or odd is also known as parity.

#### Identifying even or odd number

1. By comprehending the number at “ones” place

In this approach, we analyze the number at “ones” place in an integer to check if the number is even or odd.

All the numbers ending with 1,3,5,7 and 9 are odd numbers. For example, numbers such as 11, 23, 35, 47 etc. are odd numbers.

All the numbers ending with 0,2,4,6 and 8 are even numbers. For example, numbers such as 14, 26, 32, 40 and 88 are even numbers.
How do arrays relate to repeated addition?
Arrays are objects we put into rows and columns.

By Rows
4 + 4 + 4 = 12
By Columns
3 + 3 + 3 + 3 = 12

Tell about plants or animals that you see in groups. Look for patterns.

Plants are one of six big groups (kingdoms) of living things. They are autotrophic eukaryotes, which means they have complex cells, and make their own food. Usually they cannot move (not counting growth). Plants include familiar types such as trees, herbs, bushes, grasses, vines, ferns, mosses, and green algae.
Domestic animals such as dogs, cats, and cattle have been genetically adapted over generations to live alongside humans. Domesticated animals are animals that have been selectively bred and genetically adapted over generations to live alongside humans. They are genetically distinct from their wild ancestors or cousins.

Make an array of a group of plants and an array of a group of animals.

Review What You Know

Vocabulary
Question 1.
Circle the addends in the math below.
5 + 8 = 13
8 – 5 = 3

Question 2.
Complete the sum in the equation below.
5 + 7 = ________
5 + 7 = 12

Question 3.
Write the doubles fact that the model shows.

Explanation:- There are total 14 cubes and upper one contains 7 cubes and lower one contains 7 cubes. So, total double facts are 14.

Near Doubles
Question 4.
Find each sum.
7 + 6 = ________
4 + 5 = ________
9 + 8 = ________
7 + 6 =  13
4 + 5 =  9
9 + 8 = 17

Question 5.
Change the order of the addends and complete both equations.
6 + 8 = ________
________ + ________ = ________
6 + 8 = 14
8 + 6 = 14

Math Story
Question 6.
Five brown cows go into the barn. Then 8 black and white cows go into the barn. How many cows are now in the barn?
Answer: 5 + 8 = 13
There are already 5 brown cows are in the barn and later 8 black and white cows went to the barn so the above equation satisfy.

Pick a Project

PROJECT 2A
What kinds of birds live near you?
Project: Collect Bird Data

1. Lesser Flamingo
3. Indian Roller
5. Common Kingfisher
6. Grey Junglefowl
7. Knob-billed Duck
8. Grey Heron
9. Rose-ringed Parakeet
10. Peacock
11. Red-wattled Lapwing
12. Crested Serpent Eagle
13. Black Stork
14. Blue-tailed Bee-eater
15. Lesser Whistling-duck

PROJECT 2B
What are scutes?
Project: Make a Scutes Poster

Answer:- Scutes means an external bony or horny plate or large scale.

PROJECT 2C
How can you arrange trees in an orchard?
Project: Create an Orchard Model

A careful plan of the orchard is necessary for the most efficient and economic management. The following points should be borne in mind in preparing the plan.
1. Optimum spacing to accommodate maximum number of trees per unit area.
2. Stores and office building in the orchard should be constructed at the centre for proper supervision. .
3. Wells should be located at convenient places in different parts at the rate of one well for 2 to 4 hectares..
4. Each kind of fruit should be assigned in a separate block.
5. Fruits ripening at the same time should be grouped together.
6. Pollinators should be provided in deciduous fruits. In deciduous fruit trees, there are some varieties which require pollen from another variety to set fruits in them, otherwise, they will be barren. Such pollen donors are known as pollinators..Every third tree in every third row should be planted with a pollinator.
7. Irrigation channels should be laid along the gradients for most economical conduct of water. For every 30m length of channel, 7.5 cm slope should be given.
8. Roads should occupy minimum space for the economy of transport. The clearance between wind break and first row of trees is advantageous for the road.
9. Short growing trees should be allotted at the front and tall at the back for easy watching and to improve the appearance.
10. Evergreen trees should be in the front and deciduous ones behind.
11. Fruits attracting birds and animals should be close to the watchman’s shed.

PROJECT 2D
Project: Draw a Picture of Flowers

Flowering plants produce seeds that are then dispersed from their parent. When a seed comes to rest in an appropriate place with conditions suitable to its germination, it breaks open. The embryo inside the seed starts to grow into a seedling. Roots grow down to anchor the plant in the ground. Roots also take up water and nutrients and store food. A shoot grows skywards and develops into a stem that carries water and nutrients from the roots to the rest of the plant. The stem also supports leaves so they can collect sunlight. Leaves capture sunlight to make energy for the plant through the process of photosynthesis.

### Lesson 2.1 Even and Odd Numbers

Solve & Share
Use cubes to make the numbers below. Shade all the numbers that can be shown as two equal groups of cubes. What do you notice about the numbers you shaded?
I can … tell if a group of objects is even or odd.

Visual Learning Bridge

Convince Me! You break apart a tower of cubes to make two equal parts, but there is one cube left over. Is the number of cubes even or odd? Explain.

The total number of cubes are 15 which is odd because when we break the whole cube into two pieces one is left uneven and
the total number of cubes cannot be divide by two. So that is the reason the one is left unpair.

Guided Practice

Look at the number. Circle even or odd. Then write the equation.
Question 1.

Question 2.

Independent Practice

Look at the number. Circle even or odd. Then write the equation. Use cubes to help.
Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

For each number, circle true or false. Then explain your thinking.
Question 9.
Higher Order Thinking Dave says 12 is even. He says 21 is odd. True or false?

Explanation:- Dave says 12 is even. He says 21 is odd. Yes, He says 12 is even which is true because 12 divides by 2 and he also
says 21 is odd and this is also true because 21 does not divide by 2. So, both the statements are True.

Problem Solving

Solve the problems below. Use cubes to help.
Question 10.
Model Gemma fills 2 baskets with 9 berries each. She gives both baskets to Alan. Does Alan have an odd or even number of berries? Draw a picture to solve. Then write an equation.
_______ + _______ = _________
Alan has an _________ number of berries.

Alan has an 18 number of berries. He has even number of berries.

Question 11.
Model Tyrone puts 4 marbles in one jar. He puts 3 marbles in another jar. Does Tyrone have an odd or even number of marbles? Draw a picture to solve. Then write an equation.
_______ + _______ = _________
Tyrone has an _________ number of marbles.

Tyrone has an 7 number of marbles. Tyrone has odd number of marbles.

Question 12.
Higher Order Thinking If you add two odd numbers, will the sum be odd or even? Explain. Use numbers, pictures, or words.

Explanation:- If we add any two odd numbers the sum will always be even. We can take above image as example.
ex. 3 + 3 = 6, here 3 is an odd number and when we add those we got even number which is divisible by 2.

Question 13.
Assessment Practice Look at the number. Circle even or odd. Then write the equation.

### Lesson 2.2 Continue Even and Odd Numbers

Solve & Share
The students in Ms. Jenn’s class work in pairs. One student does not have a partner. How many students could be in Ms. Jenn’s class? Use cubes to show your thinking. Draw a picture of your work.
I can … use different ways to tell if a group of objects shows an even or odd number.

Visual Learning Bridge

Convince Me! Is the number 10 even or odd? Draw a picture to show how you know.

Explanation:- The 10 number is perfectly even because it is divided by 2 and which the remainder remains 0. So, 10 is even.

Guided Practice

Write the number for each model. Circle even or odd. Then write the equation.
Question 1.

Question 2.

Independent Practice

Write the number for each model. Circle even or odd. Practice Then write the equation.
Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.
Number Sense How many squares are shown? Is this an even or odd amount? Draw a picture that shows how you know. Write an equation for your picture.

Problem Solving

Solve the problems below. Draw pictures, if needed.
Question 10.
Look for Patterns Equations for the first four even numbers are given. What are the next six even numbers? How do you know?
1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
4 + 4 = 8
1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
4 + 4 = 8
5 + 5 = 10
6 + 6 = 12
7 + 7 = 14
8 + 8 = 16
9 + 9 = 18
10 + 10 = 20
Explanation:- These equations are sequence of natural numbers 1,2,3,4,5,6,7,8,9,10 respectively as they asked only 6 extra equations
we have done only up to 10. If we add 2 even numbers also we get even number as answer if we add 2 odd numbers also we will
get 2 odd numbers only.

Question 11.
Higher Order Thinking Mack drew a picture of 5 and 3. He says you can add them to get an even number. Do you agree? Explain and write an equation for the sum.

Answer:- I do agree with Mack because he say when we add up two odd numbers we get even number actually when we add two odd numbers we get even number for example.,
5 + 3 = 8. Here, 5 and 3 are odd numbers and the quotient is even number.

Question 12.
en Vision® STEM Desert birds are active in the early morning to stay out of the heat. Marcy sees 19 birds. Does Marcy see an odd or even number of birds? Explain with a drawing and an equation.
Answer: Marcy see and odd number of birds early in the morning.
10 + 9 = 19

Question 13.
Assessment Practice How many squares are shown? Is this an even or odd amount?

A. 6 + 6 = 12; even
B. 6 + 7 = 13; odd
C. 7 + 7 = 14; even
D. 7 + 8 = 15; odd
A. 6 + 6 = 12; even

### Lesson 2.3 Use Arrays to Find Totals

Solve & Share
Show and explain two different ways to find how many circles in all.
I can … find the total number of objects in a set of rows and columns.

Visual Learning Bridge

Convince Me! Is this group an array? Explain.

Answer:- Yes, The above image is an array because in the image the oranges were arranged in rows and columns even in one row the orange is missing. The horizontal line is row and the vertical line is column.

Guided Practice

Write two equations that match each array.
Question 1.

Question 2.

By Rows
_________ + _________ = _________
By Columns
_________ + _________ + _________ = _________
By Rows
3 + 3 + 3 = 9
By Columns
3 + 3 + 3 = 9

Independent Practice

Write two equations that match each array.
Question 3.

By Rows
_____ + _____ + _____ + _____ + _____ = _____
By Columns
_____ + _____ + _____ = _____
By Rows
3 + 3 + 3 + 3 + 3 = 15
By Columns
5 + 5 + 5 = 15

Question 4.

_____ + _____ + _____ = _____
_____ + _____ + _____ + _____ = _____
By Rows
4 + 4 + 4 = 12
By Columns
3 + 3 + 3 + 3 = 12

Question 5.

By Rows _____ + _____ = _____
By Columns _____ + _____ = _____
By Rows
2 + 2 = 4
By Columns
2 + 2 = 4

Question 6.

_____ + _____ + _____ + _____ + _____ = _____
_____ + _____ + _____ + _____ + _____ = _____
By Rows
5 + 5 + 5 + 5 + 5 = 25
By Columns
5 + 5 + 5 + 5 + 5 = 25

Question 7.
Algebra Use the array to find the missing number.

______ + 5 = 10
5 + 5 = 10

Problem Solving

Use an array to solve each problem.
Question 8.
Look for Patterns Ross places the berries in an array. Write two equations that match the array. How many berries are there in all?

________ berries
By Rows
4 + 4 + 4 + 4 + 4 = 20
By Columns
5 + 5 + 5 + 5 = 20
There are total 20 berries.

Question 9.
The array shows cars in a parking lot. Can you write two different equations that match the array? Explain. How many cars are in the parking lot in all?

_________ cars
By Row
3 + 3 + 3 = 9
By Columns
3 + 3 + 3 = 9
There are total 9 cars and they are arranged in rows and columns in each row there are 3 cars and they are 3 rows as well as there 3 cars placed in column and 3 columns are there so total 3  x 3 = 9 or 3 + 3 + 3 = 9

Question 10.
Higher Order Thinking Draw a garden with up to 5 rows and that has the same number of flowers in each row. Then write two equations that match your array.

By Rows
4 + 4 + 4 + 4 + 4 =  20
By Columns
5 + 5 + 5 + 5 = 20

Question 11.
Assessment Practice Blake sets basketballs in an array. He has 4 rows of basketballs with 3 basketballs in each row. Which equation shows the array Blake made and how many basketballs in all?
A. 3 + 3 + 3 + 3 = 12
B. 3 + 3 = 6
C. 4 + 4 = 8
D. 3 + 3 + 3 = 9
A. 3 + 3 + 3 + 3 = 12
There are total 12 basketballs in all.

### Lesson 2.4 Make Arrays to Find Totals

Solve & Share
Rusty places his toy trucks in 4 columns. He places 3 trucks in each column. How many trucks does Rusty have in all? Show how you know with counters and an equation.
I can … make arrays with equal rows or equal columns.

Visual Learning Bridge

Convince Me! If you have 2 rows with a different amount in each row, do you have an array? Explain.
Answer:- If we have 2 rows and with different amount in each row also the objects will be in rows and columns only if we have 2 rows and in one row we have 2 objects and in 2nd row we have only one object means i.e., we have 2 rows and 1 column
By Row
2 + 1 = 3

Guided Practice

Draw an array to show each problem. Use repeated addition to solve.
Question 1.
Monica puts cans of peas in 2 rows with 3 cans in each row. How many cans of peas does she have in all?

Answer: There are 6 cons of peas.

Question 2.
Dominick is organizing his stickers in columns. He has 4 columns with 4 stickers in each column. How many stickers does he have in all? _____ + _____ + _____ + _____ = _____ stickers
4 + 4 + 4 + 4 = 16
We have 16 stickers in all.

Independent Practice

Draw an array to show each problem. Use repeated addition to solve.
Question 3.
Sarah bakes loaves of bread. She places them in 5 columns with 3 loaves in each column. How many loaves of bread does Sarah have in all?
_____ + _____ + _____ + _____ + _____ = _____ loaves of bread
3 + 3 + 3 + 3 + 3 = 15
Sarah does have 15 loaves of bread in all.

Question 4.
Kristin makes an array with her books. She places them in 5 rows with 4 books in each row. How many books does Kristin have in all?
_____ + _____ + _____ + _____ + _____ = _____ books
4 + 4 + 4 + 4 + 4 = 20
Kristin does have 20 books in all.

Question 5.
Malcolm puts his marbles in two columns. He puts 2 marbles in each column. How many marbles does Malcolm have in all?
_____ + _____ = _____ marbles
2 + 2 = 4
Malcolm does have 4 marbles in all.

Question 6.
Algebra Find the missing numbers. Frank has 10 baseball cards. He places them in 2 equal rows. Show how many baseball cards are in each row.
_____ + _____ = 10 baseball cards
5 + 5 = 10 baseball cards.

Problem Solving

Draw an array to show each problem. Use repeated addition to solve.
Question 7.
Reasoning Jenny has 5 rows on each page in her photo album. She puts 2 pictures in each row. How many pictures does she have on each page?
_____ + _____ + _____ + _____ + _____ = _____ pictures
2 + 2 + 2 + 2 + 2 = 10 pictures.

Question 8.
Reasoning Nina has a bookcase with 4 shelves. She places 5 dolls in a row on each shelf. How many dolls does Nina have in all?
_____ + _____ + _____ + _____ = _____ dolls
5 + 5 + 5+ 5 = 20 dolls
Nina have 20 dolls in all

Question 9.
Higher Order Thinking Write a story problem using repeated addition. Draw an array to match your story.
Answer: We have to always multiply rows into columns or columns into rows. So, we will get total number of objects.

Question 10.
Assessment Practice Whitney has a muffin tin with 2 rows. Each row has 4 muffins. Write an equation that shows how many muffins Whitney has in all.
How can drawing a picture help?
Answer: There are 8 muffin tins with Whitney.

### Lesson 2.5 Problem Solving

Model with Math
Solve & Share
There are 4 rows in a classroom. Two rows have 3 tables in each row. Two rows have 4 tables in each row. How many tables are there in all?
Draw a picture and write an equation to model and solve the problem.
I can … model problems using equations, drawings, and arrays.
Equation: ________
_______ tables

By Rows
3 + 3  = 6
4 + 4  = 8
By columns
2 + 2 + 2 = 6
2 + 2 + 2 + 2 = 8
Total there are 14 tables.

Thinking Habits
How can a picture and an equation help me model problems?

Visual Learning Bridge

Convince Me! How does drawing a picture and writing an equation help you model a problem?
Answer:- By representing units of measurement and other objects visually, students can begin to think about the problem mathematically. Pictures and diagrams are also good ways of describing solutions to problems; therefore they are an important part of mathematical communication.

Guided Practice

Draw a picture and write an equation to show each problem. Then solve.
Question 1.
Ray has 2 rows of books. He has 5 books in each row. How many books does Ray have in all?

Independent Practice

Draw a picture and write an equation to show each problem. Then solve.
Question 2.
Mika has 4 rows of playing cards. If there are 4 playing cards in each row, how many cards does Mika have in all?
________ cards
Equation: __________
Mika has 4 rows of playing cards. If there are 4 playing cards in each row, how many cards does Mika have in all?
16 cards
By Row
4 + 4 + 4 + 4 = 16

Question 3.
Anita puts 10 baseball cards in an array. If there are 2 cards in each column, how many columns are there? Your equation should show the total number of cards.
________ columns
Equation: ________
Anita puts 10 baseball cards in an array. If there are 2 cards in each column, how many columns are there? Your equation should show the total number of cards.
10 columns
By Columns
2 + 2+ 2 + 2 + 2 + 2 + 2 + 2 + 2 = 20

Question 4.
Tina drew an array to show 9 shells. The same number of shells are in each row and each column. How many shells are in each row and each column? Explain how you know.
Answer: There  are  total 3 rows and 3 columns and each row has 3 objects that means 9 shells.
By Row
3 + 3 + 3 = 9
By Column
3 + 3 +3 = 9

Problem Solving

Window Displays Mr. Miller’s Hobby Shop has 3 window displays. One is for posters, one is for paint cans, and one is for crayon boxes. The displays are described at the right. Which display has the least number of items?

Answer: Crayon boxes has the least number of items
2 + 2 + 2 + 2 +2 = 10

Question 5.
Make Sense What are you asked to find?
Answer: To find which display has the least number of items.

Question 6.
Explain Mr. Miller says he will add 3 + 5 to find the total number of posters in the posters display. Do you agree with his plan? Explain.
Answer: No, I do not agree with Mr. Miller because we should always multiply rows and columns we should never add up them.

Question 7.

### Topic 2 Fluency Practice Activity

Color a path from Start to Finish. Follow the sums and differences that are odd numbers. You can only move up, down, right, or left.
I can … add and subtract within 20.

### Topic 2 Vocabulary Review

Understand Vocabulary
Word List

• array
• column
• doubles
• equation
• even
• odd
• row
• sum

Choose a term from the Word List to complete each sentence.
Question 1.
An _______ number cannot be shown as pairs of cubes.
An odd number cannot be shown as pairs of cubes.

Question 2.
An _________ is a group of objects set in equal rows and columns.
An array is a group of objects set in equal rows and columns.

Question 3.
In an array, objects that are shown across are in a ____________
In an array, objects that are shown across are in a  rows and columns

Question 4.
____________ are numbers that are added.

Write T for true or F for false.
Question 5.
_______ 9 is an even number.

Question 6.
_______ 13 is an odd number.

Question 7.
________ You can model repeated addition with an array.

Question 8.
________ In an array, objects that are shown up and down are in a column.

Use Vocabulary in Writing
Question 9.
Which model could you use to show 4 groups of 5 objects in each group? Use at least 1 term from the Word List.

### Topic 2 Reteaching

Set A

You can use cubes to tell if a number is even or odd.

Circle even or odd. Then write the equation. Use cubes to help.
Question 1.

Question 2.

Set B

You can use repeated addition to find the total number of loaves.

Write two equations that match the array.
Question 3.

Rows: ______ + ______ + ______ + ______ = ______
Columns
______ + ______ + ______ + ______ + ______ = ______
By Row
5 + 5 + 5 + 5 = 20
By Column
4 + 4 + 4 + 4 + 4 = 20

Set C

You can draw arrays and use repeated addition to solve problems.
Alli sets 3 rows of cans in her pantry. She puts 4 cans of beans in each row. How many cans of beans does Alli have in all?

Draw an array to show the problem. Use repeated addition to solve.
Question 4.
Steven puts 3 rows of apples on a table. Each row has 5 apples. How many apples does Steven put on the table?
______ + ______ + ______ = ________ apples

Set D

Thinking Habits
Model with Math
Can I use a drawing, array, table, or graph to model the problem?
Can I write an equation to show the problem?

Draw a model and solve the problem.
Question 5.
There are 3 columns of cars. Each column has 3 cars. How many cars are in the parking lot?
______ + ______ + ______ = ______ cars
Answer: 3 + 3 + 3 = 9 cars

### Topic 2 Assessment Practice

Question 1.
José writes an equation. The sum is an even number greater than 14.
Which equation does José write?
A. 6 + 6 = 12
B. 6 + 7 = 13
C. 8 + 8 = 16
D. 8 + 7 = 15
C. 8 + 8 = 16

Question 2.
Jen has 2 rows of apples with 4 apples in each row.
Which equation shows how many apples Jen has in all?
A. 4 + 2 = 6
B. 2 + 2 + 2 = 6
C. 4 + 4 = 8
D. 4 + 4 + 4 = 12
C. 4 + 4 = 8

Question 3.
Choose Yes or No to tell if the sum in the equation is an even number.

Question 4.
Will has 3 rows of trees in his yard. Each row has 4 trees. How many trees in all?
Draw a picture to show the array of trees.
Then write an equation for your picture.
_______ + ______+ _______ = ________
There are _______ trees in all.
4 + 4 + 4 = 12
There are 12 trees in all.

Question 5.
How many squares are shown? Is the number even or odd?

Draw a picture to show how you know.

Explanation:- Total there are 7 number of cubes and 7 is the odd number because 7 doesn’t divisible by 2.

Question 6.
Ben has 8 pennies. Look at each equation. . Choose Yes or No to tell if Ben can use the equation to make an array with his pennies.

Question 7.
Becky drew this bar diagram to show 2 equal groups can make 14.

Part A
Draw a picture to show what the “?” stands for.

Part B
Change 14 to 16 in the bar diagram. What does the “?” stand for now? Tell how you know.

Explanation:- If we replace 14 with 16 and if we divide 16 with 2 then the answer will be 8.

School Garden
Students are planting a garden at school. The pictures show the number of some plants in the garden.

Question 1.
Is there an even or odd number of tomato plants in the garden?
even
odd
Use the pictures of tomatoes to show how you know. Explain your thinking below.

Explanation:-  There are total 11 tomato plants and I have divided 11 by 2 and which is not divisible so came to know that it is odd number.

Question 2.
Tom says the number of corn plants is an even number. Do you agree? Draw a picture to show why or why not.

Explanation:- Yes, I do agree with Tom the corn plants are even because 8 is divided by 2.

Question 3.
David plants peas in the school garden. He plants 4 rows of peas with 3 plants in each row.
Part A
Draw an array to show how David planted the peas.

Part B
Write an equation to match the array. How many pea plants does David plant?
By Rows
3 + 3 + 3 + 3 = 12
By Columns
4 + 4 + 4 = 12

Question 4.
Jesse says there are other ways to make an array of 12 plants. Show an array of 12 plants that is different from the array David used.

Question 5.
The array below shows the number of pepper plants in the garden.

Add the number of plants in each row. How many pepper plants are in the garden?
______ + ______ + ______ + ______ + ______ = ______
_________ pepper plants
Is the number of pepper plants an even or an odd number?
even
odd