## Envision Math Common Core Grade K Answers Key Topic 4 Compare Numbers 0 to 10

**Essential Question:** How can numbers from 0 to 10 be compared and ordered?

**enVision STEM Project: Weather Changes**

**Directions** Read the character speech bubbles to students. Find Out! Have students find out about weather changes. Say: The weather changes from day to day. Talk to friends and relatives about the weather. Ask them to help you record the number of sunny days and rainy days during the week. Journal: Make a Poster Have students make a poster. Have them draw up to 10 lightning bolts above one house and up to 10 lightning bolts above another house. Ask them to write the number of lightning bolts above each house, and then draw a circle around the number that is greater than the other, or draw a circle around both numbers if they are the same.

**Review What You Know**

Question 1.

Answer:

Explanation:

I circled the group of birds that are lessthan the other group.3 is lessthan 4.

Question 2.

Answer:

Explanation:

I circled the group of dogs that is greater than the ther group.5 is greater than 1.

Question 3.

Answer:

Explanation:

I circled 2 groups of marbles that are equal in number.3 is equal to 3.

Question 4.

Answer:

Explanation:

There are 6 objects in the above picture.So, i counted and wrote 6.

Question 5.

Answer:

Explanation:

There are 8 objects in the above picture.So, i counted and wrote 8.

Question 6.

Answer:

Explanation:

There are 10 objects in the above picture.So, i counted and wrote 10.

**Directions** Have students:** 1** draw a circle around the group of birds that is less than the other group; **2** draw a circle around the group of dogs that is greater than the other group; **3** draw a circle around the two groups that have an equal number of marbles; **4-6** count the number of objects, and then write the number to tell how many.

**Pick a Project**

**Directions** Say: You will choose one of these projects. Look at picture A. Think about this question: How can you train to go into space? If you choose Project A, you will act out an exercise skit. Look at picture B, Think about this question: What kinds of fruit would you put into a fruit salad? If you choose Project B, you will create a fruit salad recipe.

**Directions** Say: You will choose one of these projects. Look at picture C. Think about this question: What is the most exciting ride at a theme park? If you choose Project C, you will design a ride. Look at picture D. Think about this question: What do you like to do on a vacation? If you choose Project D, you will make a list.

### Lesson 4.1 Compare Groups to 10 by Matching

**Solve & Share**

**Directions** Say: Work with a partner. Take turns drawing one cube from the bag and placing it on your page in the rectangle of the same color. When the bag is empty, do you have more red or blue cubes? How do you know? Draw a picture of your cubes in The rectangles showing which color is more.

**Visual Learning Bridge**

**Guided practice**

Question 1.

Answer:

Explanation:

I drew a line from each chick in the top group to a chick in the bottom group, and then drew a circle around the group that is greater in number than the other group.7 is greater than 6.

**Directions 1** Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group.

Question 2.

Answer:

Explanation:

I compared the groups, drew a line from each chick in the top group to a chick in the bottom group, and then drew a circle around the group that is greater in number than the other group.8 is greater than 3.

Question 3.

Answer:

Explanation:

I compared the groups, drew a line from each chick in the top group to a chick in the bottom group, and then drew a circle around the group that is less in number than the other group.4 is less than 5.

Question 4.

Answer:

Explanation:

I compared the groups, drew a line from each chick in the top group to a chick in the bottom group, and then drew a circle around the group that is less in number than the other group.7 is less than 9.

**Directions 2 envision ^{®} STEM** Say: Chicks live in coops. Coops protect chicks in different types of weather. Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is greater in number than the other group.

**3**and

**4**Have students compare the groups, draw a line from each chick in the top group to a chick in the bottom group, and then draw a circle around the group that is less in number than the other group.

**Independent Practice**

Question 5.

Answer:

Explanation:

I compared the groups, drew a line from each bucket in the top group to a bucket in the bottom group, and then drew a circle around the group that is greater in number than the other group.8 is greater than 6.

Question 6.

Answer:

Explanation:

I compared the groups, drew a line from each bucket in the top group to a bucket in the bottom group, and then drew a circle around the group that is less in number than the other group.2 is less than 3.

Question 7.

Answer:

Explanation:

I compared the groups, drew a line from each bucket in the top group to a bucket in the bottom group, and then drew a circle around the group that is less in number than the other group.4 is less than 7.

Question 8.

Answer:

Explanation:

I counted the numbe rof buckets, there are 5 buckets in the top group.

I drew a group of 9 buckets that is greater than the buckets in the top group.

9 is greater than 5.

**Directions** Have students: **5** compare the groups, draw a line from each bucket in the top group to a bucket in the bottom group, and then draw a circle around the group that is greater in number than the other group; **6** and** 7** compare the groups, draw a line from each bucket in the top group to a bucket in the bottom group, and then draw a circle around the group that is less in number than the other group, **8 Higher Order Thinking** Have students draw a group of buckets that is greater in number than the group shown.

### Lesson 4.2 Compare Numbers Using Numerals to 10

Answer:

Explanation:

Emily is planting seedlings, or little plants. She plants 5 red pepper seedlings and 7 yellow pepper seedlings.

I drew counters to show groups of seedlings and i wrote the numbers 5 and 7.I circled 7 as it is greater than 5.

**Directions** Say: Emily is planting seedlings, or little plants. She plants 5 red pepper seedlings and 7 yellow pepper seedlings. Use counters to show the groups of seedlings. Write the numbers, and then circle the number that tells which group has more.

**Visual Learning Bridge**

**Guided Practice**

Question 1.

Answer:

Explanation:

I drew a line from each watering can in the top group to a watering can in the bottom group, and then draw a circle around the number 4 as it is greater than 3.

**Directions 1** Have students count the watering cans in each group, write the number to tell how many, draw a line from each watering can in the top group to a watering can in the bottom group, and then draw a circle around the number that is greater than the other number.

Question 2.

Answer:

Explanation:

I counted the vegetables in each group, wrote the numbers 4 and 5 to tell how many, drew a line from each vegetable in the top group to a vegetable in the bottom group, and then marked an X on the number 4 as it is less than 4.

Question 3.

Answer:

Explanation:

I counted the vegetables in each group, i drew 3 more pea pods to make the groups equal, wrote the numbers 6 to tell how many in each group, and then drew a line from each vegetable in the top group to a vegetable in the bottom group to compare.

**Directions 2** Have students count the vegetables in each group, write the number to tell how many, draw a line from each vegetable in the top group to a vegetable in the bottom group, and then mark an X on the number that is less than the other number. **3 Number Sense** Have students count the vegetables in each group, draw more pea pods to make the groups equal, write the numbers to tell how many in each group, and then draw a line from each vegetable in the top group to a vegetable in the bottom group to compare.

**Independent Practice**

Question 4.

Answer:

Explanation:

I counted the seed packets in each group, wrote the numbers 10 and 7 to tell how many, drew a line from each seed packet in the top group to a seed packet in the bottom group, and then mark an X on the number 7 as it is less than 10.

Question 5.

Answer:

Explanation:

I counted the flowers in the group, drew a group of 3 flowers that is less than the group shown, and then write the numbers 6 and 3 to tell how many.

**Directions 4** Have students count the seed packets in each group, write the number to tell how many, draw a line from each seed packet in the top group to a seed packet in the bottom group, and then mark an X on the number that is less than the other number. **5 Higher Order Thinking** Have students count the flowers in the group, draw a group of flowers that is less than the group shown, and then write the numbers to tell how many.

### Lesson 4.3 Compare Groups to 10 by Counting

**Solve & Share**

Answer:

Explanation:

I counted and placed counters on goldfish and tetras, there are 6 goldfish and 9 tetras.I drew a circle around the number 9 as it is greater than 6.

**Directions** Say: The class aquarium has two kinds of fish, goldfish and tetras. Place counters on the fish as you count how many of each kind. Write numbers to tell how many of each kind. Draw a circle around the fish that has a number greater than the other. Tell how you know you are right.

**Visual Learning Bridge**

**Guided Practice**

Question 1.

Answer:

Explanation:

I counted and wrote the number of fishes each color, there are 10 pink fishes and 8 purple fishes.I circled 10 as it is greater than 8.

**Directions 1** Have students count the number of each color fish, write the numbers to tell how many, and then draw a circle around the number that is greater than the other number. Use the number sequence to help find the answer.

Question 2.

Answer:

Explanation:

I counted and wrote the number of fishes each color, there are 6 green fishes and 7 yellow fishes.I circled 7 as it is greater than 6.

Question 3.

Answer:

Explanation:

I counted wrote the number of fishes each color, there are 8 blue fishes and 9 gold fishes.I marked X on both the numbers as they are NOT equal.

Question 4.

Answer:

Explanation:

I counted wrote the number of fishes each color, there are 8 brown fishes and 7 green fishes.I marked X on the number 7 as it is lessthan 8.

Question 5.

Answer:

Explanation:

I counted wrote the number of fishes each color, there are 9 purple fishes and 10 gold fishes.I marked X on the number 7 as it is lessthan 10.

**Directions** Have students count the number of each color fish, write the numbers to tell how many, and then: **2** draw a circle around the number that is greater than the other number; **3** draw a circle around both numbers if they are equal, or mark an X on both numbers if they are NOT equal; **4** and **5** mark an X on the number that is less than the other number. Use the number sequence to help find the answer for each problem.

**Independent Practice**

Question 6.

Answer:

Explanation:

I counted and wrote the number of each critter.I wrote the numbers 6 to tell that there are 6 yellow and 6 green critters.I circled both the numbers as they are equal.

Question 7.

Answer:

Explanation:

I counted and wrote the number of each critter.I wrote the numbers 9 and 8 to tell that there are 9 blue and 8 peach critters.I marked X on the numbe 8 as it is lessthan 9.

Question 8.

Answer:

Explanation:

There are 7 trantulas in the above picture so, i drew 9 spiders that is two more than the number of trantulas.

Then i wrote the numbers 7 and 9.

Question 9.

Answer:

Explanation:

I counted the number of butterflies.There are 6 butterflies.I wrote all the numbers up to 10 that are greater than the number of butterflies shown.The numbers that are greater than 6 are 7, 8, 9 and 10.

**Directions** Have students count the number of each critter, write the numbers to tell how many, and then: **6** draw a circle around both numbers if they are equal, or mark an X on both numbers if they are NOT equal; **7** mark an X on the number that is less than the other number; 8 draw a group of spiders that is two greater in number than the number of tarantulas shown, and then write the number to tell how many. **9 Higher Order Thinking** Have students count the butterflies, and then write all the numbers up to 10 that are greater than the number of butterflies shown. Use the number sequence to help find the answer for each problem.

### Lesson 4.4 Compare Numbers to 10

**Solve & Share**

**Directions** Say: Emily’s mother asked her to bring the towels in off the line. Her basket can hold less than 7 towels. How many towels might Emily bring in? You can give more than one answer. Show how you know your answers are right.

Answer:

Emily’s mother asked her to bring the towels in off the line. Her basket can hold less than 7 towels.

Emily can bring 1, 2, , 4, 5 or 6 towels in her basket.

**Visual Learning Bridge**

**Guided Practice**

Question 1.

Answer:

Explanation:

I counted the numbers 1 to 10. I used the number sequence and drew lines from the numbers to the sequence and i circled 8 a sit is greater than 7.

Question 2.

Answer:

Explanation:

I drew counters to show the numbers 6 and 4.I drew a circle around the number 6 as it is greater than the number 4.

**Directions** Have students: **1** count the numbers 1 to 10 and use the number sequence to show how they know which number is greater than the other, and then draw a circle around the number that is greater; **2** draw counters in the ten-frames to show how they know which number is greater than the other, and then draw a circle around the number that is greater.

Question 3.

Answer:

Explanation:

I drew pictures to show the numbers 6 and 9.9 is greater than 6.

Question 4.

Answer:

Explanation:

I drew counters to show the numbers 8.

I circled both the numbers as they are equal.

Question 5.

Answer:

Explanation:

I used the number sequence to find the greater number.I marked X on the number 9 as it is lessthan 10.

Question 6.

Answer:

Explanation:

I drew the pictures to show the numbers 9 and 8.I marked X on the number 8 as it is lessthan 9.

**Directions** Have students: **3** draw pictures to show how they know which number is greater than the other, and then draw a circle around the number that is greater; **4** draw counters in the ten-frames to show how they know if the numbers are equal, and then draw a circle around both numbers if they are equal, or mark an X on both numbers if they are NOT equal; **5** use the number sequence to show how they know which number is less than the other number, and then mark an X on the number that is less; **6** draw pictures to show how they know which number is less than the other number, and then mark an X on the number that is less.

**Independent Practice**

Question 7.

Answer:

Explanation:

I drew the pictures to show the numbers 6 and 8.I marked X on the number 6 as it is lessthan 8.

Question 8.

Answer:

Explanation:

I used the number sequence to find the greater number.I marked X on the number 7 as it is lessthan 9.

Question 9.

Answer:

Explanation:

I wrote the next two numbers that are greater than 8. the numbers that are greater than 8 are 9 and 10.

Question 10.

Answer:

Explanation:

I wrote the number 7 as it is greater than 5 and lessthan 9.

**Directions** Have students: **7** draw pictures to show how they know which number is less than the other number, and then mark an X on the number that is less; **8** use the number sequence to show how they know which number is less than the other number, and then mark an X on the number that is less. **9 Higher Order Thinking** Have students write the next two numbers that are greater than the number shown, and then tell how they know. **10 Higher Order Thinking** Have students write a number that is greater than the number on the left, but less than the number on the right.

### Lesson 4.5 Repeated Reasoning

**Problem Solving**

**Solve & Share**

Answer:

**Directions** Say: There are 7 fish in a bowl. Emily puts I more fish in the bowl. How many fish are in the bowl now? How can you solve this problem?

**Visual Learning Bridge**

**Guided Practice**

Question 1.

Answer:

Explanation:

I drew counters for 4 frogs and i drew one more.The number that is one greater than 4 is 5.

**Directions 1** Say: Carlos sees 4 frogs at the pond. Then he sees 1 more. How many frogs are there now? Have students use reasoning to find the number that is 1 greater than the number of frogs shown. Draw counters to show the answer, and then write the number. Have students explain their reasoning.

**Independent Practice**

Question 2.

Answer:

Explanation:

I drew counters for 7 frogs and i drew one more.The number that is one greater than 7 is 8.

Question 3.

Answer:

Explanation:

I drew counters for 2 frogs and i drew one more.The number that is one greater than 2 is 3.

Question 4.

Answer:

Explanation:

I drew counters for 8 frogs and i drew one more.The number that is one greater than 8 is 9.

Question 5.

Answer:

Explanation:

I drew counters for 6 frogs and i drew one more.The number that is one greater than 6 is 7.

**Directions** Say: Alex sees frogs at the pond. Then he sees 1 more. How many frogs are there now? **2-5** Have students use reasoning to find the number that is 1 greater than the number of frogs shown. Draw counters to show the answer, and then write the number. Have students explain their reasoning.

**Problem Solving**

**Performance Task**

Question 6, 7, 8.

Answer:

Explanation:

I drew counters for 5 pets of Marta, i drew 1 more counter.The number that is one greater than 5 is 6.Marta will now have 6 pets.

**Directions** Read the problem aloud. Then have students use multiple problem-solving methods to solve the problem. Say: Marta’s family has 5 pets. Then her family gets 1 more. How many pets do they have now? **6 Generalize** Does something repeat in the problem? How does that help? **7 Use Tools** What tool can you use to help solve the problem? Use the tool to find the number of pets in Marta’s family now. **8 Make Sense** Should the answer be greater than or less than 5?

### Topic 4 Vocabulary Review

Question 1.

Answer:

Explanation:

I circled the number 9 as it is greater than 7.

Question 2.

Answer:

Explanation:

I counted the counters given, there are 7 counters in all.so, i wrote the number 7 in the blank.

Question 3.

Answer:

Explanation:

The number that means NONE is 0.

Question 4.

Answer:

Explanation:

There are 2 red cubes and 3 yellow cubes.I circled the red cubes as they are less than yellow cubes.I wote the number 2 as it is lessthan 3.

**Directions Understand Vocabulary** Have students: **1** draw a circle around the number that is greater than 7; **2** count the counters, and then write the number to tell how many; **3** write the number that means none; **4** count how many of each color cube there is, draw a circle around the group that has a number of cubes that is less than the other group, and then write the number to tell how many there are in that group.

Question 5.

Answer:

Explanation:

I circled the number 8 as it is greater than 3 and marked X on the number 3 as it is lessthan 8.

Question 6.

Answer:

Explanation:

I wrote 4 as it is greater than 3 and lessthan 5.

Question 7.

Answer:

Explanation:

I drew counters for the given number 5.

Question 8.

Answer:

Explanation:

I wrote the missing numbers 3, 4, 6, 7 and 8 in the gien blanks.

**Directions Understand Vocabulary** Have students:** 5** compare the numbers, draw a circle around the number that is greater, and then mark an X on the number that is less; **6** write a number that is greater than 3, but less than 5; **7** draw 5 counters in a row and then write the number to tell how many; **8** write the missing numbers in order.

### Topic 4 Reteaching

**Set A**

Question 1.

Answer:

Explanation:

I counted the number of counters, there are 6 red counters and 10 yellow counters.I circled red counters frame as they are less in number than the yellow counter frame.

**Set B**

Question 2.

Answer:

Explanation:

I drew lines from the top group to a piece of fruit in the bottom group, and then i drew a circle around the number 7 as it is greater than 5.

**Directions** Have students: **1** compare the groups, and draw a circle around the group that is less in number than the other group; **2** count the fruit in each group, write the numbers that tell how many, draw a line from each piece of fruit in the top group to a piece of fruit in the bottom group, and then draw a circle around the number that is greater than the other number.

**Set C**

Question 3.

Answer:

Explanation:

I counted and wrote the number of blue critter and peach critters.They are 6 peach critters and 4 blue critters.

I marked X on the number 4 as it is lessthan 6.

**Set D**

Question 4.

Answer:

Explanation:

I drew counters for the 6 frogs and drew one more counter.1 greater than 6 is 7.

**Directions** Have students: **3** count the number of each critter, write the numbers, and then mark an X on the number that is less than the other number; **4** Say: April sees frogs at The pond. Then she sees 1 more. How many frogs does she see now? Have students use reasoning to find the number that is 1 greater than the number of frogs shown. Draw counters to show the answer, and then write the number.

### Topic 4 Assessment Practice

Question 1.

Answer:

Explanation:

There are 8 yellow birds.I marked group ‘A’ as it has more number of blue birds than the yellow birds.There are 10 blue bieds in group A.

Question 2.

Answer:

Explanation:

I marked the numbers 6, 5 and 3.The numbers 3, 5 and 6 as they are lessthan the number 7.

Question 3.

Answer:

Explanation:

I counted and wrote the number of lemons and limes, there are 7 lemons and 5 limes.

I circled the number 7 as it is greater than 5.

**Directions** Have students mark the best answer. **1** Which group of blue birds is greater in number than the group of yellow birds? **2** Look at the number line. Then mark all the numbers that are less than the number on the card. **3** Have students count the number of lemons and limes, write the number that tells how many of each, and then draw a circle around the number that is greater.

Question 4.

Answer:

Explanation:

The number of the first card is 7, the number before 7 is 6.I counted forward from 6 and wrote the numbers 7, 8, 9 and 10 in the blanks.

Question 5.

Answer:

Explanation:

There are 6 sandwiches and I drew the 4 juice boxes as 4 is lessthan 6.

Question 6.

Answer:

Explanation:

I drew counters for 7 beads and drew 1 more counter.one greater than the number 7 is 8.

Kayla will now have 8 beads to make a bracelet.

**Directions** Have students: **4** write the number that is counted first among the 4 number cards, and then count forward and write the number that is 1 greater than the number before; **5** count the sandwiches in the group, draw a group of juice boxes that is less than the group of sandwiches shown, and then write the numbers to tell how many. **6** Say: Kayla has 7 beads to make a bracelet. Then she buys 1 more. How many beads does she have now? Have students use reasoning to find the number that is 1 greater than the number of beads shown. Draw counters to show the answer, and then write the number to tell how many.

### Topic 4 Performance Task

Question 1.

Answer:

Explanation:

There are 9 shunks and 8 raccoons in the forest.

Using number sequence i found that number 8 is lessthan number 9 so, i marked X on the number 8.

**Directions** Forest Animals Say: The forest is home to woodland animals. One part of the forest has many different animal homes in it. **1** Have students study the picture. Say: How many skunks live in this part of the forest? How many raccoons live in this part of the forest? Count the number of each type of animal and write the numbers. Then have students draw a circle around the number that is greater than the other number and mark an X on the number that is less than the other number. Have them use the number sequence to help find the answers.

Question 2.

Answer:

Explanation:

There are 6 foxes in the forest.I counted and wrote the numbers between 6 and 10.They are 7, 8, 9 and 10.

Question 3.

Answer:

Explanation:

I drew counters for the number 5, I drew circle around both the numbers as they are equal.

Question 4.

Answer:

Explanation:

There are 7 birds in the forest.I drew counters for 7 birds and one more counter as 1 bird flies into the forest.

One greater than the number 7 is 8.

**Directions** Have students look at the picture on the page before. **2** Say: How many foxes live in this part of the forest? Count how many and write the number. Then have students write all the numbers through 10 that are greater than the number of foxes. **3** Say: 5 chipmunks and 5 frogs move out of this part of the forest. Draw a circle around both numbers if they are equal, or mark an X on both numbers if they are NOT equal. Show how you know you are correct. **4** Say: How many birds live in this part of the forest? Count how many and write the number. I more bird flies into the forest. How many birds are in this part of the forest now? Have students use tools to solve the problem and write the number. Then have them show how they found the answer.