Early Math Counts

• The book, Quack and Count by Keith Baker.
• Sets of seven manipulatives (Rubber ducks would be ideal, but anything will work. You will need a set of seven manipulatives for every child.)
• A blank 10-page book with a cover that reads: Ways to Count to 7  (The easiest way to make the book is to staple together 10 blank pages of white copy paper. Staple the pages along the left, long side of the paper to create the spine of the book.)
• An easel with paper or a white board
• The song, “Little Ducks Went Out to Play”

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.

1. Explain to the children that today they are going to be working with the number seven. They will be exploring all of the different ways to make seven.
2. Ask the children to use their fingers to represent the number seven. Give the children enough time to count out the number and, when everyone has their answers, show the children the number seven on your own fingers. Give the children who were unsure or held up the incorrect number of fingers time to adjust their fingers. Say: “Great! Now that we all know how to represent the number seven, we are going to explore all of the different ways in which we can make the number seven.”
3. Introduce the book, Quack and Count, by explaining that the book is going to show us seven ducklings having fun. Sometimes the seven ducklings break up into two groups, but there are always seven ducklings having fun. Explain that their job, while reading the book, is to identify the different ways that seven ducklings can break up into smaller groups.”
4. Read the book. Pause after each grouping of ducklings is identified. When book reads: “Seven ducklings, 5 plus 2, playing games of peekaboo,” ask a child to come up and count out the five ducklings and then the two ducklings. (The book does a nice job of dividing the ducks onto two pages.) Say: “So, you have counted two ducklings on this page and five ducklings on this page. Are there still seven ducklings altogether? Let’s count.” In unison, count out all seven ducklings. Say: “So, it looks like five ducklings plus two ducklings equals seven ducklings. Does everyone agree with this?”
5. Check in. From time to time, it is important to engage in a check-in to make sure that all of the children are understanding and following along with the lesson and concepts that are being addressed. When you solve a problem or state an answer (e.g., “So it looks like five ducklings plus two ducklings equals seven ducklings. Does everyone agree with this?), you have an opportunity to ensure that everyone is on the same page. If a child says that he/she does not agree or does not understand how five plus two equals seven, then it is necessary to solidify this understanding without jeopardizing the attention of the group. You do this by asking one of the children who understands the numerical equation to explain his/her understanding to the group. This not only gives the confused child another approach to the same problem, but gives other children a chance to explain their mathematical thinking.

1. Explore the sets of seven. Have the children arrange the manipulatives in groups that represent seven. Remind the children of what you all read in the book. Say: “Six ducklings and one duckling playing slip and slide.” Using your objects, represent six ducklings and one duckling. Make sure that the children can distinguish the two separate groups. Say: “I see that you have a group of six plus a group of one. Six plus one equals seven.” Use the easel with paper to write the number sentences that represent the groups of seven that the children are making: 6+1=7.
2. Introduce the concept of the property of zero. The property of zero in addition says that a number does not change when adding zero to that number. Present the children with the problem of what number to add to the number seven. “If all seven ducklings are playing Ring Around the Rosy, how many ducklings are needed to make a group of seven?” Have the children put all of their objects into one group of seven. Say: “How many more ducklings do I need to make seven? None! I already have seven ducklings. So seven plus none, or zero, equals seven.” Write this number sentence on the easel paper: 7+0=7.  There is no need to explain this as the property of zero. The important concept is that they recognize zero as a number and know how to use it and draw on it when thinking mathematically.
3. Explain to the children that they are going to make their own books of the various ways to group numbers to get to seven. They can use their manipulatives and refer back to the book, Quack and Count, to construct their own books.
4. Model how to execute a page of the book. “In the book, there were seven ducklings playing peekaboo. Five ducklings were playing over on one side (draw five ducklings on one side of the page) and there were two ducklings playing on another side (draw two ducklings on another side of the page). Make sure there is enough space to distinguish between the two groups of ducklings) Write the number sentence at the bottom of the page: 5+2=7.” Ideally, the children should have the following groupings: 0+7=7, 1+6=7, 2+5=7, 3+4=7, 4+3=7, 5+2=7, 6+1=7, 7+0=7.

5. Grouping and identifying smaller sets within a group of seven, and then drawing symbols and number sentences to represent their mathematical thinking, helps to solidify number sense and computational fluency.
6. Encourage the children to expand their thinking. If they already have the number sentence and picture that represents the equation 7+2=5, ask: “What if there were two ducklings swimming in the pool. How many more ducklings would need to be swimming to have seven ducklings swimming in the pool?” This is the commutative property.  7+2=2+7.  Again, it is not important to identify the property. The important idea is to have the children begin to recognize that addends (numbers that are added to one another) can be added in any order and the sum is always the same.
7. Extend the children’s vocabulary and the underlying mathematical operation that is being utilized by reinforcing the addition involved. When reading the book, after each group of seven is identified, restate the group in numerical terms. Example: “Slipping, sliding, having fun. Seven ducklings, six plus one. Six plus one equals seven.”
8. Extend the children’s mathematical thinking by addressing the commutative property. “Six plus one equals seven. One plus six equals seven.” Write these two number sentences on the easel paper so that the children can see the number relationships.

Additional Extensions

• Have the children observe the differences in objects within their groupings of seven. They can begin to organize their objects in an orderly arrangement. When the children have grouped the objects within their sets of seven, they can begin to identify which subset is bigger. For example: The children have grouped their objects into one group of six and one group of one. Say: “Which group is bigger? Which group is smaller?”
• There are additional pages in the book or the back sides of the pages for the children to further group their sets of seven into three groups. For example: A group of four plus a group of one plus a group of two equals seven:  4+1+2=7.
• Incorporate subtraction into the conversation. Say: “Seven ducklings are playing on the swings, three go off to play on the slide. How many ducklings are left playing on the swings: 7-3=4.”

For younger children who cannot work with the number seven, there is another book that works with the number five:

• Five Little Ducks by Penny Ives. Have the children work and sort within groups of five.
• Sing the song, “Five Little Ducks on a Bed” to the tune of “Ten Little Monkeys Jumping on a Bed.”
• Children will make a book, but the book may only have five pages.

• Plus: The addition of (e.g.,”Five plus two equals seven.”)
• Equals: To be the same in number or amount (e.g.,”Six plus one equals seven.”)
• Represents: To show or stand for (e.g.,”When you draw six ducklings and one more duckling, you are representing the number seven. The seven ducklings on the page represent the number seven.”)
• Altogether: In total; including everyone or everything (e.g.,”There are five ducklings on this page and two ducklings on the other page. How many ducklings are there altogether?”)

Early Math Glossary

Adapt Lesson for Toddlers

Toddlers may:

• Not have one-to-one correspondence
• Not be able to count beyond five
• Not yet recognize numerals

Child care providers may:

• Provide assistance when children are counting, helping them with one-to-one correspondence
• Use the number five instead of the number seven
• Help the children manipulate their objects to represent groups within five
• Use lots of repetition with the song and book
• Only use objects instead of numerals and only introduce the plus sign and the equal sign

Adapt Lesson for Preschoolers

Preschoolers may:

• Be able to work with numbers higher than seven
• Not yet recognize numerals

Child care providers may:

• Allow children to create their own books with whatever number they choose beyond seven
• Only use objects instead of numerals and only introduce the plus sign and the equal sign
• Provide cards that show a number of objects with the corresponding numeral, so the children have something to refer to when writing their number sentences