## Remainder of One

In this lesson, children will arrange them 25 cubes into groups of two, three, four and five. The children will examine the different groups and learn about the concept of a remainder.

### Math Lesson for:

Toddlers/Preschoolers
(See Step 5: Adapt lesson for toddlers or preschoolers.)

Algebra

### Learning Goals:

This lesson will help toddlers and preschoolers meet the following educational standards:

• Understand numbers, ways of representing numbers, relationships among numbers and number systems
• Understand patterns, relations and functions
• Understand meanings of operations and how they relate to one another

### Learning Targets:

After this lesson, toddlers and preschoolers should be more proficient at:

• Counting with understanding and recognizing “how many” in sets of objects
• Developing a sense of whole numbers and representing and using them in flexible ways, including relating, composing and decomposing numbers
• Understanding situations that entail multiplication and division, such as equal groupings of objects and sharing equally
• Sorting, classifying and ordering objects by size, number and other properties
• Recognizing, describing and extending patterns such as sequences of sounds and shapes or simple numeric patterns and translating from one representation to another

## Remainder of One

### Lesson plan for toddlers/preschoolers

#### Step 1: Gather materials.

• The book, A Remainder of One by Elinor J. Pinczes
• Paper lunch bags with 25 counting blocks in each bag (Each child should have one bag with 25 blocks.)
• Chart paper and markers

Note: Small parts pose a choking hazard and are not appropriate for children age five or under. Be sure to choose lesson materials that meet safety requirements.

#### Step 2: Introduce activity.

1. Explain that the queen in the book, A Remainder of One, is having a problem and she needs the children’s help. The queen needs her squadron, her army, to line up into even and equal lines. She has 25 members in her bug army.
2. Explain that the children are going to receive bags that have 25 counting blocks in them to help them solve the problem. The children are to use the blocks as we read the book.

#### Step 3: Engage children in lesson activities.

1. Begin reading the book. Stop after reading: “The troop had divided by two for the show.” Have the children take out their blocks and make two equal lines/groups. The children will be able to make two groups of 12 but will have one left over. Have the children share their findings. Record their findings on the chart paper. Read the rest of the page: “Each bug had a partner, except soldier Joe.” Ask the children: “There are 25 bug soldiers. Can they make two even and equal lines? No.” Introduce the concept of division. “So, we can say: 25 bugs divided into two groups has 12 bugs in each line with one bug left over. Is this right?” Write the division equation on the chart paper.
2. Continue reading the book. Stop after reading: “The troop had divided by three for the show.” Have the children take out their blocks and make three equal lines/groups. The children will be able to make three groups of eight, but will have one left over. Have the children share their findings. Record their findings on the chart paper. Read the rest of the page: “Each line seemed perfect. Then someone spied Joe.” Ask the children: “There are 25 bug soldiers. Can they make three even and equal lines? No. So, we can say: 25 bugs divided into three groups has eight bugs in each line with one bug left over. Is this right?” Write the division equation on the chart paper.
3. Continue reading the book. Stop after reading: “The troop had divided by four for the show.” Have the children take out their blocks and make four equal lines/groups. The children will be able to make four groups of six, but will have one left over. Have the children share their findings. Record their findings on the chart paper. Read the rest of the page: “The lines all looked even, till they spotted Joe.” Ask the children: “There are 25 bug soldiers. Can they make four even and equal lines? No. So, we can say: 25 bugs divided into four groups has six bugs in each line with one bug left over. Is this right?” Write the division equation on the chart paper.
4. Continue reading the book. Stop after reading: “Five lines of soldiers….”  Again, have the children take out their blocks and make five equal lines/groups. The children will be able to make five groups of five with no remainders. Have the children share their findings. Record their findings on the chart paper. Read the rest of the page: “…with 5 in each row… perfect at last—and that’s counting Joe.” Ask the children: “There are 25 bug soldiers. Can they make five even and equal lines? Yes. So, we can say: 25 bugs divided into five groups has five bugs in each line, with no bugs left over. Is this right?” Write the division equation on the chart paper. “Did we do our job and help the queen?”

• Present different scenarios and numbers for the children to group and divide. Use larger or smaller numbers, depending on the children’s abilities: 18, 24, 30.

#### Step 4: Math vocabulary.

• Remainder: Amount left over after dividing a number (e.g.,”The children will be able to make five groups of five with no remainders.”)
• Divide: Sharing or grouping a number into equal parts (e.g.,”So, we can say: 25 bugs divided into four groups has six bugs in each line with one bug left over.”)

#### Step 5: Adapt lesson for toddlers or preschoolers.

##### Adapt Lesson for Toddlers
###### Toddlers may:
• Still be working with one-to-one correspondence, counting and grouping
###### Home child care providers may:
• Have the children work with smaller numbers (nine is a good number to work with because there are several ways in which the children can group the number)
##### Adapt Lesson for Preschoolers
###### Preschoolers may:
• Have a command of bigger numbers and can easily work with grouping, sorting and identifying the relationships and patterns among numbers
• Understand the concept of division—grouping numbers into equal parts
###### Home child care providers may:
• Increase the number of blocks that the children divide (61 is a good number)
• Make the connection between multiplication and division. (If division is grouping numbers into equal parts, multiplication is groups of a number. Make these connections without necessarily using the terms “division” or “multiplication.” Use “groups of” to describe the inverse relation.

### Suggested Books

• A Remainder of One by Elinor J. Pinczes (Houghton Mifflin Harcourt, 2002)

### Outdoor Connections

Go outside to act out the book with the children. Work with 25 children or a number with several factors and add one more child. Have the children line up into even rows and see if there are any children who cannot be incorporated into one of the lines. Do this until all of the children are evenly grouped into an equal number of lines.