Learning Math through Play STEAM Math is our focus for this presentation Mathmatize Glossary of Math Terms Hand Out Numbers & Operation: knowing how many, learning how to count, comparing and ordering quantities, operations (add, subtract, multiply, divide), representing number Geometry & Spatial Sense: shapes (2 and 3 dimensional, recognizing and naming, manipulating), moving body and objects through space Patterns: classifying and sorting objects; recognizing, creating, and extending patterns Measurement: length, width, height, area, weight, volume, capacity, time Practice Finding the Math and Recognizing Domain Handouts on books, games, materials, language, songs Mathmatize Activity Math Activities for each domain Numbers & Operation: Human Story Board, Graphs Geometry & Spatial Sense: Positional Word Game, Eat Your Math Patterns: People Patterns, Patterns in the Environment Measurement: Water Play, Measure the room with standard and nonstandard measurement Make-N-Take for Each Domain Numbers & Operation: Pipe Cleaner Math Geometry & Spatial Sense: Craft sticks with velcro Patterns: Dot Stickers and index cards Measurement: Measurement cards

TOOLS FOR TEACHERS MATHEMATICS KNOWLEDGE & SKILLS MATH THROUGH GAMES Adults mathematize when they bring out the math in what children are doing. As children engage in daily classroom activities and routines, adults can help them relate their experiences to the mathematical knowledge and skills that are part of those activities and routines. Playing games offers children opportunities to use and apply mathematical concepts. PLAYING GAMES Teachers can use different types of games and materials to promote children’s mathematical learning. Games can vary from tabletop games and manipulatives to outdoor gross motor play. Teachers can buy commercially available products or create their own games using everyday objects and materials. Following are suggestions of games with corresponding Mathematical Knowledge & Skills domain elements that can be emphasized within the games. Type

Examples

Cards

Go Fish, Crazy Eights

Grid games

Lottos, memory

One-inch cubes, blocks, dominoes, nesting cups, Manipulatives puzzles, shapes, sorting trays, objects for sorting

Number Concepts & Quantities

Number Relationships & Operations

Geometry & Spatial Sense

Patterns

Measurement & Comparison

4 4

4 4

4 4

4 4

4 4

4

4

4

4

4

Path games

Children’s board games

4

4

4

4

4

Put-and-take games

Dice and spinners, board games

4

4

4

4

4

Physical games

Hide and Seek, Mother May I?, Red Light, Green Light

4

4

4

RESOURCES Cutler, K. M., Gilkerson, D., Parrott, S., & Bowne, M. T. (2003). Developing math games based on children’s literature. Beyond the Journal Young Children on the Web. Retrieved from http://journal.naeyc.org/btj/200301/MathGames.pdf This article illustrates how to create simple board games to support exploration of math concepts based on popular children books.

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For more information, contact us at: [email protected] or 877-731-0764 This document was prepared under Grant #90HC0002 for the U.S. Department of Health and Human Services, Administration for Children and Families, Office of Head Start, by the National Center on Quality Teaching and Learning.

SPRING 2014

TOOLS FOR TEACHERS MATHEMATICS KNOWLEDGE & SKILLS MATERIALS TO SUPPORT MATH LEARNING Number Concepts & Quantities and Number Relationships & Operations • A variety of objects (shells, buttons, game pieces, blocks, etc.) for children to count • Board games with linear number movement • Dice and counters

• Playing cards • Dominoes • Matching card sets to play concentration

Geometry & Spatial Sense • • • • • • • • •

Containers of different shapes and sizes Clean, recycled plastic lids Large boxes to climb in Tricycles, climbing toys Origami paper to fold Tracers with geometric shapes Tangram puzzles Pattern blocks Jigsaw puzzles

• • • • • • • • •

Shape sorters Picture books Materials for an obstacle course Building blocks with a variety of shapes Three-dimensional hollow shapes to fill Checkers or board games Scavenger hunt instructions or cards Hopscotch Hula hoops

• • • • • •

Art supplies, like dot stickers, paint dobbers, stamps Large, posted daily schedule Picture books Hundred board Model construction and other vehicles Card sets showing natural cycles (animal life cycles, phases of the moon)

• • • •

Measuring tools (cups, rulers, spoons, etc.) Balance scale Rain gauge Thermometer to measure air temperature

Patterns • • • • • • •

Objects for sorting (buttons, blocks, etc.) Blocks Objects from nature Signs that label things in the classroom Pendulum Photographs of things in nature Musical instruments

Measurement & Comparison • • • • •

Blocks and balls of varying weights and sizes Variety of different-size dolls and soft animals Containers of different sizes to fill Large graph paper for chart making Nesting cups, containers, boxes

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For more information, contact us at: [email protected] or 877-731-0764 This document was prepared under Grant #90HC0002 for the U.S. Department of Health and Human Services, Administration for Children and Families, Office of Head Start, by the National Center on Quality Teaching and Learning.

SPRING 2014

TOOLS FOR TEACHERS MATHEMATICS KNOWLEDGE & SKILLS MATH THROUGH SONGS AND MUSIC Adults mathematize when they bring out the math in what children are doing. As children engage in daily classroom activities and routines, adults can help them relate their experiences to the mathematical knowledge and skills that are part of those activities and routines. Singing songs and engaging in musical activities is a fun and engaging way to experience and learn early mathematical concepts. HOW SONGS AND MUSIC SUPPORT EARLY MATH LEARNING Musical activities support children’s early mathematical development and learning. As young children sing and role-play songs, play musical instruments, and move their bodies to music, they learn about patterns, sequencing, counting, spatial properties, and other mathematical concepts and skills. Select songs that have good rhythm and that come from a variety of cultures. MATH SONGS Following is a list of songs with corresponding Mathematical Knowledge & Skills domain elements that teachers can emphasize within the song.

Title

Song or movement

Five Little Ducks

Song

Five Little Monkeys

Song

Five Little Donuts

Song

Over in the Meadow

Song

Teddy Bear, Teddy Bear

Song and movement

The Ants Go Marching

Song

The Itsy Bitsy Spider

Song and movement

Twinkle Twinkle Little Star Song (Estrellita ¿dónde estás?) Where Is Thumbkin?

Song and movement

Number Concepts & Quantities

Number Relationships & Operations

Geometry & Spatial Sense

Patterns

4 4 4 4

4 4 4 4

4 4 4 4

4 4 4 4

4

4

4

4

4

4

Measurement & Comparison

4

4

4

4

4

4

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MATH SONGS IN SPANISH Number Concepts & Quantities

Number Relationships & Operations

Title

Song or movement

A La vibora de la mar (Like a Sea Snake)

Song and movement

Cinco pollitos (Five Chicks)

Song

4

4

Un elefante se balanceaba Song (An Elephant Balancing)

4

4

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Geometry & Spatial Sense

Patterns

Measurement & Comparison

4

4

4

4

For more information, contact us at: [email protected] or 877-731-0764 This document was prepared under Grant #90HC0002 for the U.S. Department of Health and Human Services, Administration for Children and Families, Office of Head Start, by the National Center on Quality Teaching and Learning.

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Glossary of Math Terms Addition: A mathematical operation in which two or more numbers are summed to yield a single number (the total). Attribute: A property or characteristic. In geometry, this refers to shape attributes. For example, attributes of triangles include three sides and three angles or corners. In measurement, attribute refers to a measurable dimension such as length, weight, or temperature. Cardinal number (Cardinality): The number that describes the total quantity of objects (or other elements) in a group. In counting a group of objects, the cardinal number is the last number spoken. This number answers the question “how many?” Comparing and ordering (in measurement): Process of comparing two or more objects by attributes such as length, weight, area, or capacity to determine which is longer or shorter, heavier or lighter, covers more or covers less, or holds more or holds less. See Direct comparison. Comparing and ordering numbers: The process of determining which of two groups of objects has more or if they are the same, or determining which of two numbers is greater than the other (e.g., 6 is greater than 5). Understanding the relationship (more than, fewer/less than, same as or equal to) between quantities of objects or spoken numbers is an important aspect of young children’s developing number sense. Composing and decomposing numbers: Discovering the many ways that a number can be put together (composed) and taken apart (decomposed). For example, 5 objects can be decomposed to make a group of 2 objects and a group of 3 objects (or 4 and 1). Composing and decomposing shapes: Discovering the ways that shapes can be combined or divided to make other shapes. For example, two congruent right triangles can be put together to compose a square. A square can be decomposed into two triangles by drawing a line diagonally from corner to corner. Concrete object: A visible, touchable thing. Continuous quantity: An amount that is not made up of discrete, countable items. We measure continuous quantities like length, weight, or time by applying countable units like inches, pounds, or minutes. Dimension: A measurable attribute such as length, width, depth, or height.

Direct comparison: A measurement strategy for comparing the length, area, weight, or capacity of two or more objects. For example, two pencils can be directly compared to determine which one is longer by placing them side by side with the ends aligned. Discrete quantity: Refers to an amount that is made up of individual, countable items such as blocks, drumbeats, or words. Division: A mathematical operation that involves grouping or sharing a quantity into equal parts. The quantity that remains (if any) after equal groups are made is called the remainder. Children practice early division skills when they share snack or toy items fairly with their classmates. Geometric shapes: Two- and three-dimensional shapes whose attributes, such as number of sides, number of angles, and number of dimensions, are described and studied in geometry. There are many examples, including triangles, circles, squares, prisms, spheres, and cubes. Geometry: The area of mathematics that concerns space and shape. Growing pattern: A pattern in which there is a predictable change in number or size. An example is the “plus one” pattern in which each unit in the sequence has one more element than the one preceding it (e.g., A, AA, AAA, AAAA). Learning environment: Any setting or situation in which a child might be learning—during play, daily routines, planned experiences, and social interactions at home, school, or in the community. A mathematics learning environment is any setting or situation in which a child might be learning math. Manipulatives: Concrete objects used to support math learning. For example, counting bears are manipulatives that can be used for practicing counting, sorting by color and size, duplicating and creating patterns, simple addition and subtraction with objects, and for supporting many other mathematical concepts and skills. Mathematize: To highlight mathematical concepts in everyday experiences. Multiplication: A mathematical operation in which a quantity is added to itself a certain number of times. For example, 3 times 2 (3 X 2) is three 2s added together (2 + 2 + 2). Non-standard measurement: Measuring that does not involve a standardized unit (inch, pound, etc.). For example, children might measure their heights using non-standard units such as blocks, or they might use lengths of string to measure and compare the size of two pumpkins.

Non-standard measurement tool: Any item used as a non-standard unit for measuring. See Non-standard measurement. Number: Describes a countable quantity. Number word: Spoken, written, or signed word that represents a quantity, such as “one,” “two,” or “three.” Numeral: A written symbol that represents a number, such as 1, 2, or 3. One-to-one correspondence: Matching one object, word, or action to another object, word, or action (one for one). In counting objects, one-to-one correspondence refers to matching one and only one number word to each item being counted. Operations: Addition, subtraction, multiplication, and division of numbers. Ordinal number: A number word that describes the order of objects, for example, “first,” “second,” or “third.” Part-whole relations: The relationship between a whole number and its parts (the smaller numbers that compose it). See Composing and decomposing numbers. Pattern: A regular, predictable arrangement of things. Objects, numbers, sounds, actions, or events can make a pattern. (See Repeating pattern and Growing pattern.) Repeating pattern: A pattern in which a sequence of elements (see core unit) is repeated again and again without change, such as “red stripe-white stripe, red stripe-white stripe, red stripe-white stripe.” Representing number: Showing numerical information using concrete objects such as blocks, dice, and fingers; spoken number words such as “four”; or written symbols such as a numeral (4) or tally marks (/ / / /). Sequencing: Arranging a set of items in order, according to a rule. For example, stones or other collected objects can be put in order from smallest to largest or largest to smallest. Numbers in the counting sequence are ordered by increasing value. Spatial relations: The direction, position, order, or orientation of objects in relation to other objects. See Spatial reasoning. Spatial reasoning (spatial thinking; spatial sense): Thinking about how objects fit together and can be moved in space, as well as how one’s body fits and moves in relation to objects in the environment. Spatial concepts include directionality, position, order, and location of people and objects in space and the words that describe these concepts. Standard measurement: Measuring with standardized or standard units such as inches, pounds, or degrees using tools like rulers, scales, and thermometers.

Standard measurement tool: A device that is used to apply standardized units to an attribute. For example, a ruler is used to measure the length of an object in inches or a scale is used to measure a person’s weight in pounds. See Standard measurement. Subitizing: Identifying the number in a very small group of objects perceptually, by looking or touching, without needing to count. Subtraction: A mathematical operation in which a quantity is removed or taken away from another. The resulting number is the difference between the starting number and the number taken away. For example, subtracting 2 from 5 leaves 3, which is the difference between 5 and 2. Symmetry: An object is symmetrical when dividing it in half produces two parts that are mirror images of each other. Three-dimensional (3-D) shapes: In geometry, shapes that have height, width, and depth dimensions. 3-D shapes can be measured with units of volume like cubic inches. Examples include spheres, cubes, and prisms. More information about 3-D shapes is provided in the handout, “Two- and Three-Dimensional Shapes, Attributes, and Properties.” Two-dimensional (2-D) shapes: In geometry, shapes that have length and width dimensions, but no depth. 2-D shapes can be measured with units of area like square inches. Examples include triangles, circles, squares, and parallelograms. More information about 2-D shapes is provided in the handout, “Two- and Three-Dimensional Shapes, Attributes, and Properties.”

TOOLS FOR TEACHERS MATHEMATICS KNOWLEDGE & SKILLS MATHEMATICS VOCABULARY AND PHRASES Here are some words and phrases adults can include in daily activities to strengthen children’s early mathematical learning. Use these words and phrases as you make comments about what children are doing, ask questions about what children are interested in, and expand on what children say. Number Concepts & Quantities • Count

• All together

• A few

• One, two, three, four, five

• A lot

• How many?

• One more

• Add/subtract

• Share

• One less

• Same as

• First, second, last

• In

• Under

• Below

• Out

• Up

• Over

• On

• Down

• Around, in front of

• Last

• Above

• Behind

• Next

• Top

• Next to, beside

• First, second

• Bottom

• Between, through

• Far

• Near

• Inside

• Flip

• Rotate

• Outside

Number Relationships & Operations

Geometry & Spatial Sense

• Slide

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Patterns • What comes next?

• Let’s read the pattern together

• Grow

• What came before?

• Repeat

• Increase • Decrease

Measurement & Comparison • How is this ____ different than that____?

• Weight

• Distance

• Height

• Speed

• Which of these _____ is bigger than the other? How do you know?

• Length

• Temperature

• Width

• Hotter, colder

• How much more/less?

• More, less

• Bigger, smaller

• Heavier, lighter

• Taller, shorter

• Volume

• Louder, softer

• Circumference

• Faster, slower

• Amount

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For more information, contact us at: [email protected] or 877-731-0764 This document was prepared under Grant #90HC0002 for the U.S. Department of Health and Human Services, Administration for Children and Families, Office of Head Start, by the National Center on Quality Teaching and Learning.

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LEARNING ACTIVITY MATHEMATICS KNOWLEDGE & SKILLS PRACTICE AND PLAN TO MATHEMATIZE What does it mean to “mathematize?” When teachers mathematize they bring out the math in what children are doing by commenting or questioning. Did you know? • Preschool teachers’ math talk correlates with children’s gains in math knowledge over a school year. • When teachers mathematize, they are helping children acquire “the language of mathematics,” which also affects their mathematical skills. What are some ways to start mathematizing? • Ask problem-solving questions. Asking children to solve practical problems that emphasize mathematical thinking promotes their higher-order thinking skills and enlists them as contributing members of the classroom. An example of a problem-solving question might be, “What do you think will help you fill your bowl with yogurt the fastest, this small spoon or this medium-sized ladle? Which one do you want to use?” • Have back-and-forth exchanges. When children offer their mathematical ideas, use back-and-forth exchanges to understand their thinking, encourage their language skills, and clarify their understanding of certain concepts. An example of a mathematical back-and-forth exchange might be: Sara: Teacher Carrie! Look! I made a house. Teacher Carrie: You constructed a house using the blocks! It looks very sturdy. How would you describe your house? What shape is it? Sara: Well, it’s kind of squarish, and tall, and pointy at the roof. Teacher Carrie: What makes this house squarish? Sara: Its sides go like this: one, two, three, four (tracing each of the four sides), like a big square. • “Revoice” children’s ideas. Revoicing means saying a phrase or idea back to a child using similar language and asking the child if that is correct. An example of revoicing might be, “So you’re saying that when we add all the apples together, we have eight?” Revoicing children’s ideas can help teachers check their understanding of what children are saying and can also help children explain more clearly.

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How can I practice mathematizing? Look at each of the following pictures. How would you mathematize this moment with a child? Think of the domain elements of Mathematics Knowledge & Skills—Number Concepts & Quantities, Number Relationships & Operations, Geometry & Spatial Sense, Patterns, and Measurement & Comparison—and then whether you would use a problemsolving question, back-and-forth exchange, and/or “revoicing” to extend the child’s math learning. Write down a few ideas about how you might mathematize in each situation.

Problem-solving questions, back-and-forth exchanges, and/or revoicing children’s ideas: 1.

2.

3.

 

2

Problem-solving questions, back-and-forth exchanges, and/or revoicing children’s ideas: 1.

2.

3.

 

3

Planning to mathematize! Think of three areas of the room where you will look for opportunities to mathematize with children: 1.

2.

3.

What materials will you add to these areas to help children engage in play and exploration that also includes mathematical ideas? 1.

2.

3.

References Kazemi, E. (2003). Classroom practices that support children’s mathematical ideas. In C. Howes (Ed.), Teaching 4- to 8-year olds: Literacy, math, multiculturalism, and classroom community (pp. 113–134). Baltimore, MD: Paul H. Brookes Publishing. Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children’s mathematical knowledge: The effect of teacher “math talk.” Developmental Psychology, 42(1), 59–69.

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For more information, contact us at: [email protected] or 877-731-0764 This document was prepared under Grant #90HC0002 for the U.S. Department of Health and Human Services, Administration for Children and Families, Office of Head Start, by the National Center on Quality Teaching and Learning.

SPRING 2014

TOOLS FOR TEACHERS MATHEMATICS KNOWLEDGE & SKILLS MATH THROUGH BOOKS Adults mathematize when they bring out the math in what children are doing. As children engage in daily classroom activities and routines, adults can help them relate their experiences to the mathematical knowledge and skills that are part of those activities and routines. Reading books is a common preschool activity that offers children varied opportunities to practice and explore mathematical concepts. CHOOSING BOOKS Many children’s books lend themselves to teaching mathematical concepts. There are two main types of books to consider when selecting books to support mathematical learning. Some books focus directly on mathematical concepts such as counting or shapes. Other books have mathematical concepts embedded within the story or illustrations. When choosing picture books, use both types of books. Look for pictures and stories that offer opportunities for children to practice early mathematical skills such as counting, recognizing shapes and patterns, measuring, and comparing. Be sure to use books that represent a variety of languages and cultures. Here is a list of children’s books with suggestions of Mathematical Knowledge & Skills domain elements addressed in the book. Title/author

Story

A Triangle for Adaora by I. Onyefulu

Two girls explore shapes of objects in their village.

Anno’s Counting by M. Anno

Landscapes change through various times of day and seasons.

Cubes, Cones, Cylinders & Spheres by T. Hoban

Photographs show shapes in everyday life.

Five Creatures by E. Jenkins

Three people and two cats form a family.

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Number Concepts & Quantities

Number Relationships & Operations

Geometry & Spatial Sense

Patterns

Measurement & Comparison

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4

4 4

4

4 4

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Title/author

Story

Goodnight Moon (Buenas noches, luna) by M. W. Brown

A bear goes to sleep.

Inch by Inch by L. Lionni

An inchworm measures things.

Quack and Count by K. Baker

Ducklings have fun.

Rosie’s Walk (El paseo de Rosie) by P. Hutchins

Rosie the hen goes for a walk around the farm.

The Carrot Seed (La semilla de zanahoria) by R. Krauss & C. Johnson

A boy plants a carrot seed and watches it grow.

Number Concepts & Quantities

Number Relationships & Operations

4

Geometry & Spatial Sense

Patterns

4

4

Measurement & Comparison

4 4

4 4 4

The Doorbell Rang People come to (Llaman a la puerta) Ma’s to share her by P. Hutchins wonderful cookies.

4

The First Day of Winter by D. Fleming

A boy decorates a snowman.

4

The Secret Birthday Message (El mensaje secreto de cumpleanos) by E. Carle

A boy follows a map to find a birthday surprise.

The Three Bears (Tres osos) by various authors

A girl visits a house of bears.

4

We’re Going on a Picnic by P. Hutchins

Animals go on a picnic.

4

4

4

4 4

4

4 4

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USING BOOKS TO TEACH MATH For more suggestions on how to use books to promote math learning, take a look at the following resources from Erickson Institute’s Early Math Collaborative: A Triangle for Adaora by Ifeoma Onyefulu http://earlymath.erikson.edu/a-triangle-for-adaora/ Anno’s Counting Book by Mitsumo http://earlymath.erikson.edu/numbers-and-fun-with-annos-counting-book/ The First Day of Winter by Denise Fleming http://earlymath.erikson.edu/the-first-day-of-winter/ The Secret Birthday Message by Eric Carle http://earlymath.erikson.edu/exploring-geometry-with-the-secret-birthday-message/ The Three Bears (various authors) http://earlymath.erikson.edu/three-bears-sort-in-a-dual-language-classroom/ We’re Going on a Picnic by Pat Hutchins http://earlymath.erikson.edu/its-picnic-time-dont-forget-to-pack-the-math/

RESOURCES These materials provide suggestions for math-related children’s books and ways to use books to create games. Cutler, K. M., Gilkerson, D., Parrott, S., & Bowne, M. T. (2003). Developing math games based on children’s literature. Beyond the Journal Young Children on the Web. Retrieved from http://journal.naeyc.org/btj/200301/MathGames.pdf This article illustrates how to create simple board games to support exploration of math concepts based on popular children books. Dickinson, P. (2003). Choosing books you can count on. Beyond the Journal Young Children on the Web. Retrieved from http://journal.naeyc.org/btj/200301/ChildrensBooks.pdf This is an annotated list of picture books that introduce children to number concepts and operations.

3

PLANNING FORM: MATHEMATIZING CHILDREN’S BOOKS Use this form to plan for small group or circle time story book reading. Copy examples of comments and questions onto sticky notes and place on corresponding book pages as reminders. Book title

Storyline or main idea

Stopping points and key comments and questions Page number:

Extension activities

Adapted from: Hintz, A., & Smith, A. (2013). Mathematizing read-alouds in three easy steps. The Reading Teacher, 67(2), 103–108. Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/TRTR.1182/pdf

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For more information, contact us at: [email protected] or 877-731-0764 This document was prepared under Grant #90HC0002 for the U.S. Department of Health and Human Services, Administration for Children and Families, Office of Head Start, by the National Center on Quality Teaching and Learning.

SPRING 2014