Math Access for Teachers and Home Child Care Providers

Quack and Count

Through the use of manipulatives, children will form different groups that make up the number 7.

Content Area Standard Target
• Algebra
• Number and Operations
• Understand numbers, ways of representing numbers, relationship among numbers, and number systems
• Compute fluently and make reasonable estimates
• Understands meanings of operations and how they relate to one another
• Understand patterns, relations, and functions
• Represent and analyze mathematical situations and structures using algebraic symbols
• Use mathematical models to represent and understand quantitative relationships
• Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations
• Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators
• Develop and use strategies for whole-number computations, with a focus on addition and subtraction
Obtain the Materials

• The book, Quack and Count by Keith Baker.
• Sets of 7 manipulatives (rubber ducks would be ideal but anything will work). Each child needs to have his/her own set of 7 to work with.
• A blank book of 10 pages with a cover that says, “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 to act as the spine of the book.
• An easel with paper or white board.
• The song, “Little Ducks Went Out to Play."

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 to the children that today they are going to be working with the number 7.  They will be exploring all of the different ways to make 7.
2. Ask the children to use their fingers to represent the number 7.  Give the children enough time to count out the number and when everyone has their answers, show the children the number 7 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 7, we are going to explore all of the different ways in which we can make the number 7.”
3. Introduce the book, Quack and Count by explaining that the book is going to show us 7 ducklings having fun.  Sometimes the 7 ducklings break up into two groups, but there are always 7 ducklings having fun.  Explain that their job, while reading the book, is to identify the different ways 7 duckling 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 5 ducklings and then the 2 ducklings. (The book does a nice job of dividing the ducks onto 2 pages)  Say: “So, you have counted 2 ducklings on this page and 5 ducklings on this page."  “Are there still 7 ducklings altogether?”  “Let’s count.”
In unison, count out all 7 ducklings.  Say: “So, it looks like 5 ducklings plus 2 ducklings equals 7 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 like, “So it looks like 5 ducklings plus 2 ducklings equals 7 duckling.  Does everyone agree with this?”  This question is an opportunity to ensure that everyone is on the same page.  If a child says that they do not agree or do not understand how 5 plus 2 equals 7, 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 their understanding to the group.  This not only provides the confused child another approach to the same problem and makes them feel secure in their uncertainty but allows other children a chance to explain their mathematical thinking.

Engage the Children

1. Explore the sets of 7.  Have the children arrange the manipulatives into groups that represent 7.  Remind them of what you all read in the book.  “6 ducklings and 1 duckling playing slip and slide.  Using your objects, represent 6 ducklings and 1 duckling.  Make sure we can tell the two separate groups."  “I see that you have a group of 6 plus a group of 1.  6 plus 1 equals 7.” Use the easel w/ paper to write the number sentences that represent the groups of 7 that the children are making.  Example: 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 7.  “If all 7 ducklings are playing Ring Around the Rosy, how many ducklings are needed to make a group of 7?”  Have the children put all of their objects into 1 group of 7.  Say: “How many more ducklings do I need to make 7?”  “None!  I already have 7 ducklings. So 7 plus none, or 0 equals 7.”  Write this number sentence on the easel paper.  Example: 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 upon it when mathematically thinking.
3. Explain to the children that they are going to make their own book of the various ways to group numbers to get to 7.  They can use their manipulatives and refer back to the book to construct their book.
4. Model how to execute a page of the book.  “In the book, there were 7 ducklings playing peekaboo.  5 ducklings were playing over on one side (draw 5 ducklings on one side of the page) and there were 2 ducklings playing on another side. (draw 2 ducklings on another side of the page."  Make sure there is enough space to distinguish between the 2 groups of ducklings)  5 + 2 = 7.  Write the number sentence at the bottom of the page.  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

1. Grouping and identifying smaller sets within a group of 7 and then drawing symbols and number sentences to represent their mathematical thinking, help to solidify number sense and computational fluency.
2. 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 2 ducklings swimming in the pool.  How many more ducklings would need to be swimming to have 7 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 can be added in any order and the sum is always the same.
3. 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 7 is identified, restate the group in numerical terms.  Example: “Slipping, sliding, having fun.  7 ducklings, 6 plus 1.  6 plus 1 equals 7."
4. Extend the children’s mathematical thinking by addressing the Commutative Property.  “6 plus one equals 7.  1 plus 6 equals 7.”  Write these two number sentences on the easel paper so that the children can see the number relationships.

• Have the children observe the differences in objects within their grouping of 7.  They can begin to organize their objects in an orderly arrangement.  When the children have grouped the objects within their set of 7, they can begin to identify which subset is bigger.  For Example: The children have grouped their objects into one group of 6 and one group of 1. Say: “Which group is bigger?”,  “Which group is smaller?”
• There are additional pages in the book or the backside of the pages for the children to further group their set of 7 into 3 groups.  For Example: A group of 4 plus a group of 1 plus a group of 2 equals 7.  4 + 1 + 2 =7.
• Include subtraction into the conversation.  Say: “7 ducklings are playing on the swings, 3 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 7, there is another book that works with the number 5.

• Five Little Ducks by Penny Ives.  Have the children work and sort within groups of 5.
• 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 5 pages.

Encourage Vocabulary

• Plus – The addition of (e.g., "5 plus 2 equals 7.")
• Equals – To be the same in number or amount (e.g., "Six plus 1 equals 7.")
• Represents – To show or stand for (e.g., "When you draw 6 ducklings and 1 more duckling, you are representing the number 7.  The 7 ducklings on the page represent the number 7.")
• Altogether – In total; including everyone or everything (e.g., "There are 5 ducklings on this page and 2 ducklings on the other page.  How many ducklings are there altogether?")

Glossary of MATH vocabulary

Supporting Children at Different Levels

Toddlers   Pre-K

Toddlers may:

• Not have one-to–one correspondence.
• Not be able to count beyond 5.
• Not yet recognize numerals.

Pre-K Children may:

• Be able to work with numbers higher than 7.
• Not yet recognize numerals.

Home child care providers may:

• Provide assistance when children are counting, helping them with one-to-one correspondence.
• Use the number 5 instead of the number 7.
• Help the children manipulate their objects to represent groups within 5.
• Use lots of repetition with song and book.
• Only use objects instead of numerals and only introduce the + sign and the = sign.

Home child care providers may:

• Allow children to create their own book with whatever number they choose beyond 7.
• Only use objects instead of numerals and only introduce the + sign and the = sign.
• Provide cards that show number of objects with the corresponding numeral so children have something they can refer to when writing their number sentences.

Books

• Quack and Count by Keith Baker (San Anselmo, CA: Sandpiper, 2004)
• Five Little Ducks by Penny Ives (Auburn, ME: Child’s Play Intl Ltd, 2007)
• Seven Little Rabbits by John Becker and Barbara Cooney (London: Walker’s Children, 2007)

Music and Movement

Outdoor Connections

• This is a great activity for water play.  You will need a water table or a small wading pool.  Fill the pool with water and have the rubber ducks floating in the pool.  As you read the book or sing the songs, you can have the children take turns acting out the lyrics.  You can also pose mathematical questions as the children play with the ducks.  Example: “There are 3 ducks in the pool and 4 ducks outside of the pool on the ground.  How many ducks are there altogether?”  “So, 3 plus 4 equals 7.”  “Now put 1 of the ducks from the ground into the pool.  How many ducks do we have in the pool?”  “How many ducks are outside of the pool on the ground?”

Web Resources

• Many great games for all age levels and abilities.  Counting to 5, 10 & 20, representing the numbers, comparing and adding with sums up to 5 and 10.
http://www.ixl.com/math/pre-k/

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