Sub-domain: Mathematics and Numeracy

The Mathematics and Numeracy sub-domain covers goals thirty-nine through forty-one of the Idaho Early Learning Guidelines. 

Using this guide

Scroll down to see the age group you are most interested in. Click on the goal to learn more about the goal's:

  • developmental growth
  • child indicators
  • caregiver strategies

There is an option to download the information at the end of each goal. When you click the link you will be brought to a new page where you can download the goal as a PDF.  

Close up of child writing

0 - 8 Months

Goal 39: Children demonstrate understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.

Developmental Growth: Begin to develop awareness of quantity.

Child Indicators: Begins to show awareness of differences between people and objects. Begins to show awareness of small quantity differences; looking at or reaching for two or more people or objects. Begins to respond to the spoken concept, “more” in reference to food or play. Shows cues of hunger and fullness. Uses gestures to request “more.” Responds by focusing on an object pointed to by someone.

Caregiver Strategies: Count objects in child’s environment “out loud” in the home language. Engage child in activities that show “more.” Use counting finger-plays, songs, and number rhymes (One, Two, Buckle My Shoe). Tell stories and read books with numbers and counting.Provide large age-appropriate magnetic numerals and multiple hand-size blocks. Respond to child’s hunger and fullness cues with either more food or by withdrawing food. Pair words for “more” with action around hunger, fullness, reaching for more toys, more hugs, or more music. Feed infants in relation to hunger and fullness cues. Comment on socks and shoes as they are put on the infant (e.g., say, “one shoe…two shoes).

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Goal 40: Children demonstrate understanding of measurable attributes of objects and the unites, systems, and processes of measurement (including, size, volume, height, weight, length, area, and time).

Developmental Growth: Show awareness of spatial relationships.

Child Indicators: Begins to show awareness of own body space. Holds, handles, and plays with toys and objects (different sizes and shapes).

Caregiver Strategies: Provide defined areas that allow for movement and exploration of personal space with materials and activities. Provide multiple containers of various sizes and shapes to fill and empty with toys and objects. Describe spatial relationships such as “in” and “out” as baby explores items. Describe and make simple comparisons such as more, less, same. Provide baby with toys that have incremental sizes (nesting cups, stackable rings) from own and other cultural backgrounds. During daily care routines, talk with the baby about their surroundings, their body movements, and what will happen next.

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Goal 41: Children demonstrate understanding of patterns, relations, and functions used to organize their world and facilitate problem-solving.

Developmental Growth: Develop awareness of sounds, sights, or motor activities that occur regularly in daily routines

Child Indicators: Develops awareness of familiar sequences of events in daily routines. Begins to develop expectations for familiar sequences of events in daily routines. Feel, handle, and explore objects with a variety of textures, shapes, and sizes. Responds to variations in sounds, smells, tastes, and touch.

Caregiver Strategies: Label patterns occurring in events and objects (describe a flower or leaf). Use language to describe patterns (describe pattern/sequence during diaper changing). Provide child with toys that involve shapes (blocks, jar lids, plastic containers). Sing songs, use finger-plays, and read books with repeatable action patterns, familiar objects, colors, and shapes; noting similarities and differences. Identify and label different shapes in child’s environment. Offer a variety of touches (gentle, firm) and textures.

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6 - 18 Months

Goal 39: Children demonstrate understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.

Developmental Growth: Manipulate objects with a variety of attributes and quantities.

Child Indicators: Notices characteristics of objects (size, color, shape, or quantity). Shows interest in real-life mathematical concepts (matching objects, lining up objects, enjoying books with numbers and counting). Begins to use symbols, signs, and language to show wanting “more” and “all gone”. Fills and dumps containers with objects. Searches for objects that are out of sight. Drops objects; then looks for the object.

Caregiver Strategies: Describe the groups/arrangements of objects that the child places together (e.g., “I see you put all the blocks together.”). Use numbers to label items (counting shoes, toes, or food) used in daily routines. Use counting finger-plays, songs, and number rhymes (one, two, buckle my shoe). Tell stories and read books with numbers and counting. Provide number/numeral materials in child’s environment (large age-appropriate magnetic numerals). Engage child in activities that show “more”. Read books that have themes such as big and little, more, all gone, and counting. Sing songs that introduce numbers and encourage the child to sing along (3 little ducks, 3 little monkeys). Provide opportunities for child to fill and dump containers with objects. Play Peek-a-Boo. Hide objects to be found.

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Goal 40: Children demonstrate understanding of measurable attributes of objects and the unites, systems, and processes of measurement (including, size, volume, height, weight, length, area, and time).

Developmental Growth: Compare spatial relationships

Child Indicators: Increases awareness of body space in relation to people and objects. Groups/arranges a few objects by size (smaller and bigger), with assistance. Fills and empties containers with objects. Nests two to three sequential cups or blocks. Takes objects apart and attempts to put them together.

Caregiver Strategies: Provide defined areas that allow for spatial movement activities according to personal space using a variety of materials. Provide multiple containers of various sizes and shapes to fill and empty with toys and objects for use in sand or water play.  Required to develop an eventual understanding of volume (filling, emptying). Model the use of language when making comparisons such as more or less, same or different and encourage child to make comparisons. Provide simple and multi-part toys such as pop beads, snap- together blocks, and simple puzzles.Request items according to size, volume, weight, and length (e.g., “Please hand me the big truck.”). Around the daily care routine, talk with child about mathematical concepts using everyday activities and language like counting fingers, toes, airplanes are big, bugs are small, who has blue on, etc.

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Goal 41: Children demonstrate understanding of patterns, relations, and functions used to organize their world and facilitate problem-solving.

Developmental Growth: Notice and respond to patterns

Child Indicators: Demonstrates expectations for familiar sequences of events in daily routines. Groups a few objects by color, shape, or size; with assistance. Begins to match simple two- dimensional shapes in form board and puzzles. Reaches for utensils when food is placed in front of them. Understands what clothing is for by putting clothing on like hats, socks, loose pants, and shirts.

Caregiver Strategies: Describe and discuss patterns occurring in daily events and familiar objects (actions used to make the jack-in-the-box pop up). Ask the child to tell, “What comes next? What happens next? What do we do next?” during daily or familiar activities and routines (getting dressed or brushing teeth). Sing songs, use finger-plays, and read books with repeated action patterns, familiar objects, colors, and shapes; asking the child to help describe similarities and differences. Ask child to help name objects, shapes, and colors found in the child’s environment. Provide opportunities for the child to sort and classify familiar objects in meaningful ways (e.g., “Pick up all of the toys that are animals.”).

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These skills are essential for children to effectively navigate mathematical situations that arise in everyday life.

16 - 38 Months

Goal 39: Children demonstrate understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.

Developmental Growth: Compare differences between two or more objects or groups of objects.  Compare differences in the quantity of objects.

Child Indicators: Matches objects by a single characteristic (size, color, shape, or quantity). Sorts objects by a single characteristic (size, color, shape, or quantity). May begin to imitate counting.  Uses some number words (one, two…). Recognizes that a single object is “one” regardless of size, shape, or other attributes. Imitates counting rhymes or songs (Five Little Monkeys). Recognizes some quantities (sees 2 blocks and says, “Two.”). Manipulates sets of up to three items. Uses words to symbolize quantity and comparisons of quantity (all, some, none, more). Understands basic common relations (toothbrush and toothpaste).

Caregiver Strategies: Use quantity concepts in everyday routines (e.g., Would you like one more or two more pieces?). Pair objects during daily activities (one child gets one snack). Provide child with math-related toys and objects from own and other cultural backgrounds, for grouping and counting.Model using math and writing numerals in daily activities (using tally marks to count children who want milk). Use counting finger-plays, songs, and number rhymes, repeatedly. Tell stories, sing songs, and read books with numbers and counting, repeatedly. Provide small table blocks and unit blocks for child to play and explore with.

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Goal 40: Children demonstrate understanding of measurable attributes of objects and the unites, systems, and processes of measurement (including, size, volume, height, weight, length, area, and time).

Developmental Growth: Order and sequence objects according to different dimensions.

Child Indicators: Uses size words, such as “many,” “big,” and “little,” appropriately. Fills and empties containers (with sand or water). Compares the size of various everyday objects (puts different people’s shoes side by side to see which is longest). Identifies objects by a single characteristic such as big or small, heavy or light, and tall or short; with assistance. Looks at two objects and identifies which one is bigger or smaller. Explores measuring tools (measuring cup, ruler). Demonstrates comparative behavior by nesting up to five cups. Orders objects by size, volume, height, weight, and length; with assistance.

Caregiver Strategies: Provide sand and water play; giving child opportunities to pour, fill, scoop, weigh, and dump.Model the use of language involving comparisons according to size, volume, weight, and height (length) of people, toys, and objects. Help child to build towers or stairs using blocks sequentially in size or height. Help child arrange toys or objects from smallest to largest or longest to shortest. Chart child’s changes in height and weight. Provide play dough for children to explore, squish, and manipulate.  Add cups and containers for children to fill.

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Goal 41: Children demonstrate understanding of patterns, relations, and functions used to organize their world and facilitate problem-solving.

Developmental Growth: Recall, group, and anticipate familiar sequences of events and use these memories to predict and respond to events.

Child Indicators: Shows recognition of sequences of events or objects. Repeats actions in sequence such as finger-plays. Plays with shape toys (the round block goes in the round hole; the square block goes in the square hole). Groups objects on the basis of visual characteristics (shape or color) or themes (functional uses such as items for scooping). Classifies everyday objects that go together (shoe/sock, pencil/paper, comb/brush). With practice and development, uses groupings to create patterns.Matches simple two-dimensional shapes in form board and puzzles (circles, squares, triangles). Identifies two geometric shapes (circle, square).

Caregiver Strategies: Locate where groups of objects belong in their surroundings (coats are hung up on coat racks or cubbies; paint is located in the art area). Ask to help put objects where they belong (e.g., “Where do keep the scissors?”  “Where do we put the trucks?”). Provide opportunities for child to notice and describe patterns in nature (patterns in rocks or shells). Use shape words in daily life (e.g., “Let’s cut the cornbread into squares.”). Identify the features of shapes when child plays with them. Provide opportunities for child to look for shapes during daily activities (e.g., “Where do you see circles?”). Provide play and art materials that have different shapes (circles, squares, triangles). Demonstrate, explain, and engage child in activities that identify culturally-specific patterning in artwork or objects. Provide opportunities to help with food preparation, following a specified pattern/sequence. Play games with pattern/sequences (Duck, Duck; Goose; and Simon Says). Ask questions and support child’s curiosity (e.g., “What do we use scissors for?”  “Do all of these rocks fit in the bucket?”  “Will the stick sink in the water?”).

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36 - 60 Months

Goal 39: Children demonstrate understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.

Developmental Growth: Use number words and concepts to explore and manipulate quantity, size, and relationship.

Child Indicators: Develops understanding of counting process (recognition and naming numerals one, two and three); counting up to ten from memory in home language (e.g., recites, “one, two, three), without assistance. Counts up to ten objects; matching numbers one-to-one with objects (cubes, toys, and pennies) within daily activities. Develops understanding that when counting items, they must be counted only once, and that none should be left out. Begins recognizing that the last number counted represents the “total objects” (for quantities up to ten).  Counting is cumulative. Applies numbers and counting concepts within daily routines (count numbers of children at the table). Applies counting to new situations (counting objects, counting groups). Demonstrates understanding that numbers represent quantity (gets three apples out of the box). Uses math concepts (more, less, some, many, all, a few, none, huge, tiny, small, smaller, large, larger) to compare quantities. May count backwards from ten. Differentiates numerals from letters. Recognizes and names some numerals (pointing to written numerals named by adult). Writes and identifies some numerals named by adult. Uses meanings of numbers to create strategies for solving problems and responding to practical situations, with assistance (e.g., “Jimmy took two crackers and I didn’t get any.”).

Caregiver Strategies: Talk aloud and engage child in meaningful counting and activities that incorporate simple math computations during daily routines (e.g., number of snacks needed for the number of children). Have child divide objects equally among a group of people (each child gets three crackers or five different color crayons). Pose math questions relevant to daily life (e.g., “How many days until your birthday?  How many days until the field trip?”). Estimate how many objects you have or will see and then count out loud (e.g., How many children are here, and who is not?). Engage the child in activities and interactions that use numbers and counting (play grocery store, engage child in recording inventories of canned goods or fish). Play culturally-appropriate card and board games using counting and number concepts with children. Make available daily puzzles and manipulative materials that link numerals to pictures to represent quantity. Provide manipulatives of varied size to meet the needs of individual children.  Modify manipulatives to make them easier for children to manipulate (add grips to stabilize or Velcro to ease placement during grouping or matching activities) as needed.Post numerals and icons (simple pictures) in the room to indicate group size limits for each learning center. Describe and explain how printed numbers have different meanings (speed limits, temperature, clock, prices). Use pictures to represent real life situations involving mathematical concepts (such as simple addition used in cooking recipes). Provide a variety of objects for the child to collect, handle, and group (buttons, stones, pine cones). Provide cooking activities with recipes that link numerals to pictures to represent quantity. Use counting finger-plays, songs, and number rhymes, repeatedly. Tell stories and read books with numbers and counting, repeatedly.

 

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Goal 40: Children demonstrate understanding of measurable attributes of objects and the unites, systems, and processes of measurement (including, size, volume, height, weight, length, area, and time).

Developmental Growth: Use geometric modeling and spatial reasoning according to different dimensions.

Child Indicators: Engages in activities that explore and develop vocabulary for measurable properties such as length and weight, or capacity. Compares amongst several objects based on one or more attributes (length, size, weight) using words such as “shorter”, “bigger”, or “lighter”. Understands positional terms such as “between”, “inside”, “over”, “under”, and “behind”. Sorts and classifies objects based on one or more attributes. Orders objects by size, volume, height, weight, and length; with assistance. Measures objects using variable nonstandard units. Begins to measure objects using standard unit (one-inch cubes, paper clips). Uses measuring tools in play activities (measuring tape, measuring cups). Measures sand or water using a variety of containers. Uses picture cookbook to follow sequence and measures amounts for cooking projects, with assistance. Uses some vocabulary in relationship to measurement tools (scale, cup, ruler).  May not have accurate understanding of meaning. Estimates size (e.g., “I’m as tall as the yellow bookshelf.”).

Caregiver Strategies: Demonstrate, explain, and engage child in activities that use nonstandard measurement (use handfuls to measure rice, use footsteps to measure distance). Demonstrate, explain, and engage child in activities that measure with nonstandard measuring units (measure wooden blocks using paper clips and compare – which one uses more paper clips?)  As child gains skill with non-standardized units of measurement, introduce standardized measuring tools.Provide a variety of measuring tools (tape measures, rulers, balance scales, measuring cups) for child to use in purposeful ways. Model and engage use of conventional measuring tools and methods in everyday situations (during cooking, art projects, grocery shopping). Continue to model language involving comparisons according to size, volume, weight, and height (length) of people, toys, and objects. Play measuring games with child (e.g., “Which is heavier?” “Which is longer?). Display information using measurement graphs to visually compare activities and experiences (such as a growth chart of all the children in the class). Model language and use body and objects using positional terms (behind, inside, on top, under).

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Goal 41: Children demonstrate understanding of patterns, relations, and functions used to organize their world and facilitate problem-solving.

Developmental Growth: Sort, classify, and order objects by color, number, size, or shape.  Form simple patterns involving color, number, size, and shape.

Child Indicators: Compares shape and size of familiar objects. Sorts and builds with two- and three-dimensional shapes (sphere, cube, cone). Identifies and labels different kinds of two-dimensional shapes (square, circle, rectangle, triangle). Draws and creates pictures using various shapes. Recognizes non-geometrical shapes in nature (clouds or other things that are not circles, squares, triangles). Describes characteristics of familiar geometric and non- geometric shapes in the environment, with assistance. Puts together and takes apart shapes to make other shapes (use two triangles to make a rectangle or square with blocks).Makes and describes patterns including serialization based on numbers, shapes, and size. Predicts what comes next in a pattern and completes the pattern. Creates or extends a complex pattern with more than two repeating elements.

Caregiver Strategies: Provide a variety of increasingly complex materials related to patterns such as puzzles and stringing beads. Provide opportunities for child to create art projects that use shapes (e.g., “You can draw a house by putting a triangle on top of a square.”  “You can draw a rectangle for the door.”). Engage the child in recognizing shapes in the environment (octagonal stop sign, bowls are circles). Provide materials that can be connected and combined to create new shapes. Take child to observe murals or other community artwork; exploring together the variety of shapes used. Provide picture recipes for children to follow and complete. Play classification games with child (gather a group of items that include pairs of objects that go together - shoe/sock, flower/vase -find the items that go together). Play matching games that challenge the child to recognize what is missing. Play games that challenge the child to describe and identify shapes. Use a sensory bag or box where the child reaches in, feels and describes an object/shape and attempts to name it. Challenge child to repeat patterns made by clapping, stomping, or with rhythm instruments. Encourage child to retell stories, recalling a sequence of events (“The Very Hungry Caterpillar” “Goldilocks and the Three Bears”). Encourage child to act out plays/skits (“Three Little Pigs” “Three Billy Goats Gruff”). Encourage child to explore ordinal numbers (first, second, third, etc., and last) used to describe members of a sequence of objects or events. Ask child to describe or explain a sequence used during a familiar activity or routine and ask, “What comes next?  “What comes last?” Provide materials in shapes that can be used to represent or recreate murals or other art forms in the community. Ask child to help with the place setting for snack or lunch. Provide storage for materials that encourage sorting clean up (labeled separate containers for pencils or markers).

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Mathematics and numeracy skills include skills for understanding and using numbers and quantity, special relations, numerous mathematical operations, measurements, and properties of ordering.

60 Months - Kindergarten

Goal 39: Children demonstrate understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.

Developmental Growth: Count with understanding.  Recognize “how many” are in sets of objects; demonstrating an understanding of discrete numbers.

Child Indicators: Tells what number comes before or after a given number up to 10. Tells what number comes before or after a given number up to 20, with assistance. Demonstrates the difference between addition (more) and subtraction (take away), with assistance. Understands that quantity is not affected by the arrangement of the objects being counted. Understands that when counting items, they must be counted only once and none should be left out. Uses numbers to predict and make realistic guesses (e.g., “I think there are about 20 marbles in that jar.”). Puts numeral cards in order 1 to 10. Counts backwards from 10. Shows the verbal, symbolic, and physical representation of a number up to 10. Understands and uses numbers in meaningful ways. Demonstrates knowledge of our numeration system by counting forward by ones to at least 31. Identifies a penny as a value of money. Selects strategies appropriate for solving a problem. Performs computation accurately. Uses concrete objects to illustrate the concepts of addition and subtraction. Estimates and judges reasonableness of results. Uses estimation to identify a number of objects and evaluates the reasonableness of an answer.

Caregiver Strategies: Estimate how many objects there are and then count out loud. Child and adult pose math questions relevant to daily life (How many days until your birthday?  How many days until the field trip?). Use printed numbers in meaningful ways (recording daily temperature for weather forecasts, posting prices for a lemonade stand or bake sale). Use pictures to represent real-life situations involving mathematical concepts (simple addition used in cooking recipes). Engage the child in activities and interactions that use numbers and counting (play grocery store, engage child in recording inventories of canned goods or fish). Have children divide objects equally among a group of people (each child gets three crackers or five different color crayons).Use counting finger-plays, songs, and number rhymes, repeatedly. Tell stories and read books with numbers and counting, repeatedly. Model writing simple math equations that are relevant to real-life situations (create and record own recipe).

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Goal 40: Children demonstrate understanding of measurable attributes of objects and the unites, systems, and processes of measurement (including, size, volume, height, weight, length, area, and time).

Developmental Growth: Order objects according to spatial attributes using nonstandard and standard units of measurement.

Child Indicators: Compares objects by measurement attributes (longer/shorter, heavy/light, more/less). Exhibits spontaneous comparison by sorting, classifying, and placing objects in series; using a variety of properties (size, volume, height, weight, and length) simultaneously. Begins to measure using standard units in the customary and metric systems (measures inches using a ruler or measuring tape). Uses picture cookbook to independently measure amounts and follow steps in cooking project. Estimates how many steps it will take to walk across the room. Uses conventional vocabulary of measurement (“pound”, “inch”, “cup”). Uses basic time vocabulary. Names days of the week. Orders events in a day. Compares temperatures (hotter/colder). Reads calendar according to days, weeks, and months.

Caregiver Strategies: Demonstrate, explain, and engage child in activities that measure with standard traditional measuring units (measure a table by inches using measuring tape). Play measuring games with child (e.g., “Which is heavier?” “Which is longer?”). Provide a variety of measuring tools (tape measures, rulers, balance scales, measuring cups) and opportunities for child to select the tool needed for an appropriate measurement (using a scale to measure the apple’s weight). Introduce graphing for children to use as a way to show sequences and quantity comparisons. Provide calendar activities to describe and discuss events according to days, weeks, and months.

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Goal 41: Children demonstrate understanding of patterns, relations, and functions used to organize their world and facilitate problem-solving.

Developmental Growth: Sort, classify, and order objects by size, number, shape, and other properties

Child Indicators: Recognizes, names, builds, compares, and sorts two- and three-dimensional shapes (sphere, cube, cone). Combines shapes to create two- dimensional figures. Describes characteristics of familiar geometric and non- geometric shapes in the environment, with assistance. Investigates and predicts the results of putting together and taking apart two- and three- dimensional shapes. Recognizes and creates shapes that have symmetry. Recognizes, describes, and extends patterns; and translates from one representation to another. Describes (using rules/generalizations) and replicates patterns. Creates own patterns applying determined rules or generalizations.

Caregiver Strategies: Provide construction materials of varying sizes and shapes for multiple purposes (color strips of paper used to create weaving patterns). Play games with visual patterns like cards, dominoes, and dice for child to recognize pattern arrangements representing specific quantities. Complete surveys for likes/ dislikes (survey child’s favorite ice cream flavor) and graph results.Record daily lunch count or weather forecasts and complete data analysis to reveal patterns. Help child draft/illustrate picture recipes for other children to use. Play classification games that encourage child to describe, compare/contrast, match, and identify objects simultaneously. Ask child to use ordinal numbers (first, second, third, etc., and last) to describe or retell stories and events (recalling a trip to the zoo). Challenge child to make predictions concerning functional patterns in daily routines and activities (e.g., “What can happen if we don’t count how many want chocolate milk?). Provide opportunities for child to observe functional patterns when adding/subtracting.

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