The Mathematics Knowledge & Skills domain describes children’s abilities to understand numbers, quantity, and the relationships between them. Also important to this domain is a basic understanding of shapes, the position of shapes in space, patterns, and measurement. Many indicators described in this domain require children to make generalizations and think abstractly, which build cognitive skills that support a wide array of early learning and are associated with positive outcomes. Some of the indicators and examples may not be appropriate until late in the 3–5 year age range.
Mathematics Knowledge & Skills
Children may . . .
Children may. . .
Adults may . . .
1. Number Concepts and Quantities: The understanding that numbers represent quantities and have ordinal properties (number words represent a rank order, particular size, or position in a list).
- Count verbally or sign to at least 20 by ones.*
- Instantly recognize, without counting, small quantities of up to five objects and say or sign the number.*
- Say or sign the number names in order when counting, pairing one number word that corresponds with one object, up to at least 10.*
- Use the number name of the last object counted to answer “How many?” questions for up to approximately 10 objects.*
- Accurately count as many as five objects in a scattered configuration or out of a collection of more than five objects.*
- Understand that each successive number name refers to a quantity that is one larger.*
- Identify whether the number of objects in one group is more than, less than or the same as objects in another group for up to at least five objects.*
- Identify and use numbers related to order or position from first to fifth.*
- Associate a number of objects with a written numeral 0–5.*
- Recognize and, with support, write some numerals up to 10.*
- Matches a group of 1 to 10 objects with written and spoken number.
- Count, group, and sort objects and materials.
- Read stories, sing songs, and act out poems and finger plays that involve counting, numerals, and shapes.
- Match a group of 1 to 5 objects with written and spoken numbers.
- Copy a printed numeral using their own handwriting.
- Play games that involve matching numerals to numbers of objects, such as dots on cards.
- Count and use numbers as you play together. Ask children to answer “How many?” to encourage children to count, compare which has more and which has less, and talk about quantity.
- Make counting part of everyday routines, like setting the table or determining the number of people in a play area.
- Have children group and order materials when cleaning up.
- Play board games with a spinner, a die or dice, and other games such as dominoes, number blocks, and cards and puzzles with numbers.
- Sing counting songs, finger plays, and read children’s books with numerical content to provide a playful context for practicing counting and understanding cardinality.
- Provide opportunities for children to write numbers that are meaningful to them, such as their age, how many people are in their family, or how many blocks they stacked to create a tall tower.
2. Operations and Algebraic Thinking: The use of numbers to describe relationships and solve problems.
- Represent addition and subtraction in different ways, such as with fingers, objects, and drawings.*
- Solve addition and subtraction problems set in simple contexts. Add and subtract up to at least five to or from a given number to find a sum or difference up to 10.*
- With adult assistance, begin to use counting on (adding 1 or 2, for example) from the larger number for addition.*
- Fill in missing elements of simple patterns.*
- Duplicate simple patterns in a different location than demonstrated, such as making the same alternating color pattern with blocks at a table that was demonstrated on the rug. Extend patterns, such as making an eight-block tower of the same pattern that was demonstrated with four blocks.*
- Identify the core unit of sequentially repeating patterns, such as color in a sequence of alternating red and blue blocks.*
- Take three away from five, counting “Five, four, three … two!” while keeping track using their fingers.
- Say after receiving more crackers at snack time, “I had two and now I have four.”
- Predict what will happen when one more object is taken away from a group of five or fewer objects, and then verify their prediction by taking the object away and counting the remaining objects.
- Use art materials and other objects to create or replicate patterns (e.g., weaving, stringing beads, stacking blocks, or drawing repeating pictures).
- Recognize patterns in a story or song.
- Identify two blocks, one red and one blue, as the core unit of a longer pattern using alternating red and blue blocks.
- Sequence story cards to show beginning, middle, and end.
- Use books, songs, and games to introduce and reinforce the concepts of addition (adding to) and subtraction (taking away from).
- Watch for opportunities to pose simple number problems during daily routines, interactions, and activities; for example:
- If you give me one crayon, how many will you have left?
- You have three apple slices. If I give you one more apple slice, how many apple slices will you have all together?
- Point out patterns in indoor and outdoor environments. Invite children to identify patterns they see.
- Invite children to create patterns physically through marching, sitting, jumping, or clapping (e.g., jump-jump-clap-clap, jump-jump-clap-clap or stand-clap-sit, stand-clap-sit). Sing songs which involve the use of physical patterns, like “If You’re Happy and You Know It, Clap Your Hands” or “Hokey Pokey.”
- Create patterns with sounds by using rhythm instruments such as shakers or sticks.
- Share books, stories, and nursery rhyme songs that have repetitive structures, phrases, or rhymes (e.g., “The Wheels on the Bus” or “Old MacDonald Had a Farm”).
3. Measurement and Data: The understanding of attributes and relative properties of objects as related to size, capacity, and area.
- Use comparative language, such as shortest, heavier, biggest, or later.*
- Compare or order up to five objects based on their measurable attributes, such as height or weight.*
- Measure using the same unit, such as putting together snap cubes to see how tall a book is.*
- Sort objects by physical characteristics such as a color or size.
- Group objects according to their size, using standard and nonstandard forms of measurement (e.g., height, weight, length, color, or brightness).
- Explore various processes and units for measurement and begin to notice different results of one method or another.
- Follow a pictorial recipe and let children measure, pour, and stir the ingredients while asking questions like, “How many cups of flour does the recipe show we need to put in the bowl?”
- Provide opportunities for children to sort, classify and group household objects and materials.
- Ask questions of measurement (e.g., “How many steps does it take to walk from the front door to your cubby?” or “How many blocks long is your arm?”).
- Offer a variety of measuring tools and models, such as rulers, yardsticks, measuring tapes, measuring cups, scales, and thermometers. (Children may not use each of these correctly, but they are developing early understandings of how tools measure things.)
- Provide opportunities for children to use non-standard measuring tools such as cubes, paperclips, blocks, etc.
4. Geometry and Spatial Sense: The understanding of shapes, their properties, and how objects are related to one another.
- Name and describe shapes in terms of length of sides, number of sides, and number of angles/corners*.
- Correctly name basic shapes (circle, square, rectangle, triangle) regardless of size and orientation.*
- Analyze, compare, and sort two-and three-dimensional shapes and objects in different sizes. Describe their similarities, differences, and other attributes, such as size and shape.*
- Compose simple shapes to form larger shapes.
- Understand and use language related to directionality, order, and the position of objects, including up/down and in front/behind.*
- Correctly follow directions involving their own position in space, such as “Stand up” and “Move forward.”*
- Match, sort, group, and name basic shapes found outside or in the classroom.
- Use pattern tiles to make shapes out of other shapes, such as putting two squares side-by-side to make a non-square rectangle.
- Put away blocks and/or tiles into different containers based on the number or length of sides.
- Use the vocabulary of geometry and position to describe shapes within the room and surrounding environment.
- Understand relational directions, such as “Please put a mat under each plate.”
- Use a sensory table with various bowls, cups, or other containers to encourage activities with shapes and sorting.
- Provide children with puzzles made of simple geometric shapes and encourage saying the names of shapes as they play.
- Discuss geometric shapes in terms of their attributes, such as “This is a circle. It’s perfectly round with no bumps or corners. This is a triangle. It has three sides and three angles.”
- Use a variety of lengths and angles in their shapes (such as scalene triangles, long and thin rectangles) as well as more common configurations of shapes (such as equilateral triangles).
- Provide opportunities for conversation using everyday words to indicate space location, shape, and size of objects, saying things like, “You crawled under the picnic table, over the tree stump, and now you are in the tunnel slide!”
- Help children organize toys, pointing out concepts such as “in,” “on,” and “beside.”