Early Math · Grades K, 1

Sorting and Counting: Groups and Graphs

Quick answer

Sorting puts things that are alike into the same group: cars with cars, balls with balls. Once the groups are sorted, each one can be counted, and the groups can be put in order from most to fewest. A graph shows the same counts as rows or bars, and it answers questions such as how many there are in all and how many more are in one group than in another.

What you'll learn

  • Sort objects into groups and count each group
  • Put groups in order from most to fewest
  • Read a graph with up to three groups to find the total and how many more or fewer

Sort into groups

Here is a toy box. It has cars, balls and blocks all mixed up.

To sort them, put the cars in one group. Put the balls in one group. Put the blocks in one group. Things that are alike go together.

Toys sorted into three groups Three rows of dots. The cars row has four dots. The balls row has six dots. The blocks row has three dots. cars balls blocks
Toys sorted into three groups

Now count each group. There are 44 cars, 66 balls and 33 blocks.

Put the groups in order

Which group has the most? The balls. There are 66 of them.

Which group has the fewest? The blocks. There are 33 of them.

In order from most to fewest: balls (66), cars (44), blocks (33).

Why sorting helps you count

In a mixed-up pile, it is hard to count the cars. You might miss one, or count one twice.

Once each kind is in its own row, you count each row once. Every toy is in one group, and each group gets counted once.

The rows help in one more way. They all start at the same spot. So the longest row has the most.

Show it on a graph

A graph shows the counts as bars. Each bar is one group. Its end tells how many.

Toys in the box A bar graph. Cars goes to 4. Balls goes to 6. Blocks goes to 3. 0 1 2 3 4 5 6 cars balls blocks
Toys in the box

The graph can tell you a lot:

  • In all: 4+6+3=134 + 6 + 3 = 13 toys.
  • How many more balls than cars? 6−4=26 - 4 = 2 more.
  • How many fewer blocks than balls? 6−3=36 - 3 = 3 fewer.

Worked examples

Common mistakes

Practice problems

  1. A box has 33 red crayons, 55 blue crayons and 22 green crayons. Which color has the most?

    Answer

    Blue

    Full solution

    55 is the biggest count, and there are 55 blue crayons.

  2. Put the crayon groups from problem 1 in order from fewest to most.

    Answer

    Green, red, blue

    Full solution

    Green has 22, red has 33 and blue has 55.

  3. How many stars are there? How many moons?

    Stars and moons Two rows of dots. The stars row has six dots. The moons row has four dots. stars moons
    Stars and moons
    Answer

    66 stars and 44 moons

    Full solution

    Count each row: 66 in the stars row and 44 in the moons row.

  4. In problem 3, how many more stars than moons?

    Answer

    22

    Full solution

    6−4=26 - 4 = 2. The stars row goes 22 dots past the moons row.

  5. Use this graph of the weather. Which kind of day was there the most of?

    Weather this month A bar graph. Rain goes to 3. Sun goes to 8. Snow goes to 1. 0 1 2 3 4 5 6 7 8 rain sun snow
    Weather this month
    Answer

    Sun

    Full solution

    The sun bar is the longest. It goes to 88.

  6. In the weather graph, how many days are there in all?

    Answer

    1212

    Full solution

    3+8+1=123 + 8 + 1 = 12 days.

  7. In the weather graph, how many fewer snow days than rain days?

    Answer

    22

    Full solution

    There are 33 rain days and 11 snow day. 3−1=23 - 1 = 2 fewer.

  8. Name two ways to sort a pile of buttons.

    Answer

    Two of: by color, by size, by shape, by how many holes.

    Full solution

    Any way that puts alike buttons together works. Big ones and small ones is one way.

  9. 66 kids like red and 66 kids like blue. Which color has more?

    Answer

    Neither. They are the same.

    Full solution

    Both groups have 66. So one is not more than the other.

  10. A graph shows 88 cats and 55 dogs. Tom says there are 88 more cats. What went wrong?

    Hint

    How far past the dogs does the cat count go?

    Answer

    He gave the cat count. There are 33 more cats.

    Full solution

    “How many more” asks for the gap. Take away: 8−5=38 - 5 = 3.

    There are 33 more cats than dogs.

Frequently asked questions

What does it mean to sort?

To put things that are alike into the same group. You can sort toys by kind, buttons by size or crayons by color.

Why sort before counting?

Each kind ends up in its own group, so you count every group once. Nothing gets missed or counted twice.

How do I put groups in order?

Count each group. The group with the biggest count has the most; the one with the smallest count has the fewest.

How do I find how many more are in one group?

Take the smaller count away from the bigger one. 7 dogs and 5 cats means 7 − 5 = 2 more dogs.

How do I find how many there are in all?

Add the counts of all the groups. Groups of 4, 6 and 3 make 4 + 6 + 3 = 13 in all.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.K.MD.B.3Measurement and DataClassify objects into given categories; count the numbers of objects in each category and sort the categories by count.
  • CCSS.MATH.CONTENT.1.MD.C.4Measurement and DataOrganize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.