Math Access for Teachers and Home Child Care Providers

Remainder of One

Using 25 cubes, children will arrange them into groups of 2, 3, 4, and 5.  Children will examine the different groups and be introduced to the concept of a remainder.

Content Area Standard Target
• Number and Operations
• Algebra
• 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
• Count with understanding and recognize “how many” in sets of objects
• Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers
• Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally
• Sort, classify, and order objects by size, number, and other properties
• Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another
Obtain the 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 create a choking hazard for children. Make sure that all materials you choose to use for an activity or lesson with children meet safety requirements. Small parts are not appropriate for children who are 5 years of age or younger.

Introduce the 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.

Engage the Children

1. Begin reading the book.  When you read, “The troop had divided by two for the show.” Have the children take out their blocks and make 2 equal lines, groups.  The children will be able to make 2 groups of 12 but will have 1 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 2 even and equal lines?”  “No.”  Introduce the concept of division. “So we can say, 25 bugs divided into 2 groups has 12 bugs in each line with 1 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 3 equal lines, groups.  The children will be able to make 3 groups of 8 but will have 1 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 3 even and equal lines?”  “No.”  “So we can say, 25 bugs divided into 3 groups has 8 bugs in each line with 1 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 4 equal lines, groups.  The children will be able to make 4 groups of 6 but will have 1 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 4 even and equal lines?”  “No.”  “So we can say, 25 bugs divided into 4 groups has 6 bugs in each line with 1 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 5 equal lines, groups.  The children will be able to make 5 groups of 5 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 5 even and equal lines?”  “Yes.”  “So we can say, 25 bugs divided into 5 groups has 5 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.  Higher or lower numbers depending on the children’s abilities. (18, 24, 30).

Encourage Vocabulary

• Remainder – Amount left over after dividing a number (e.g., "The children will be able to make 5 groups of 5 with no remainders.")
• Divide Sharing or grouping a number into equal part (e.g., "So we can say, 25 bugs divided into 4 groups has 6 bugs in each line with 1 bug left over.")

Glossary of MATH vocabulary

Supporting Children at Different Levels

Toddlers   Pre-K

Toddlers may:

• Still be working with one-to-one correspondence, counting, and grouping.

Pre-K Children 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:

• Have the children work with smaller numbers – 9 is a good number to work with because there are several ways in which the children can group the number.

Home child care providers may:

• Increase the number of blocks that they 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 “division” or “multiplication”.  Use “groups of” to describe the inverse relation.

Books

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

Music and Movement

Outdoor Connections

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

Web Resources

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