Mathematics Standard 1: 

Demonstrates mathematical concepts and skills during play and other activities.


Child knows number names and the count sequence.


Child recognizes the number of objects in a small set.

P-MATH 3.​

Child understands the relationship between numbers and quantities.


Child compares numbers.

​ P-MATH 5.

Child associates a quantity with written numerals up to 5 and begins to write numbers.

Rote counts in sequence to 5 and beyond.

  • During a game Benjamin copies an adult who says, “One, two, three!"
  • Olivia signs 1, 2, 3, 4, 5, 6 in the correct sequence as the children sing a counting song.
  • Yandi counts out loud correctly, “One, two, three, four, five…"
  • Andre counts out loud, “One, two, three, four, five, six, seven, eight, nine, ten!" as Emily runs and ​hides under the ladder on the playground.

Recognizes that a single object is always “one" regardless of size, shape, and/or other attributes.   

  • Reagan says, “There is one big rock and one little rock."
  • When her therapist asks, “Show me one block" Kendra nods at a single block.
  • Steven points to a single puzzle piece, a block, and a small ball, and says “one" each time he points to the object.

Keeps one-to-one correspondence between counting words and objects (one number word for each object) for small groups of objects.

  • Cami sets the table so that each person gets one napkin and one plate.
  • Evan counts each paper he places in each of the four cubbies.
  • Adam points to each of the animal figures arranged in a line and says a counting word for each.
  • Sophia notices crayons scattered across the table and begins counting them, picking each one up, saying a number name, and placing it on her paper as she counts.

Accurately counts a set or sets of objects to 5 and beyond and answers the question “how many".

  • When the teacher asks Willow to count the number of bears she has arranged in a line, Willow points to each bear and counts, “1, 2, 3, 4." When the teacher then asks Willow how many bears she has, Willow pauses and then responds, “Three?"
  • Samantha points to the swings and says, “One, two, three.  Three children are on the swings."
  • Mykala counts 4 blocks balanced on top of each other and signs to her friend, “Four."
  • At snack time, Colton counts the number of straws piled on the table and says, “There are five straws."
  • Elian asks Caleb how many beads he has strung on his two ribbons.  Caleb pushes both ribbons so that they are side-by-side and counts the beads on one ribbon and then the other. “One, two, three, four, five, six." He reports to Elian, “I have six beads!"
  • After rolling the die, Anthony counts out four beans.  He then rolls the die again and counts out two beans.  Last, he pushes both sets of beans together, counts all of the beans and says out loud, “Now I have six!". 

Effortlessly states the number of objects in a small collection of 1-4 items without counting.

  • Shanesha looks briefly at the plate of two crackers and immediately communicates the quantity by indicating there are two crackers.
  • When asked how many blocks are on the carpet, Adrian holds up three fingers without counting the blocks.
  • Aki rolls the die and calls out, “Four!" without counting the pips on the die.
  • When the teacher shows the class a picture of four flowers, Isabella quickly holds up 2 fingers on one hand and 2 fingers on the other to communicate that there are four flowers.

Compares two sets of 1-5 concrete objects and uses language such as more, less, or same as to describe the comparison.

  • Liam places 5 two-colored counters in a cup, shakes them, and then spills them onto the work mat where he sees 4 yellow counters and 1 red counter.  He exclaims, “Yellow won! It has more."
  • Jay has a set of yellow beads and a set of red beads. When asked which set has more, Jay pairs one red bead with a yellow bead until he runs out of red beads to pair.  “The yellow group has more because there's still some left!"
  • Tamika counts the number of rocks she has and then counts the number of rocks her friend has.  “Five and five.  You have the same as me."
  • The teacher places 5 counters onto one plate and 3 counters onto another plate, then places both plates on April's wheelchair tray and asks which plate has less. April uses her head wand to point to the plate with 3 counters.

Recognizes and identifies some numerals.

  • The teacher shows Madison a set of cards, two of which have the numeral 3 on them. Madison slides one card with the numeral 3 over to the other numeral 3 card, creating a match.
  • When the teacher asks for a volunteer to find the number 5 on the song chart, Kelly points to “5" in the title, 5 Little Bubbles.
  • Nicki sees the numeral 2 on the cash register and says, “That's two."
  • Sitting in her wheelchair near several numerals written in chalk on the ground, Ava rolls from numeral 3 and calls out “One!" as she stops on numeral 1.

Scribbles, marks, or writes numerals on the paper to represent a number or quantity.

  • As Emily takes the restaurant order, she makes squiggly marks on her pad of paper and states, “That'll be three dollars."
  • Amir draws a picture of a birthday cake and attempts to write the numeral 4 while stating, “I'm four."
  • Using a pencil with a built-up grip, Lu writes the numeral 2 while working in the writing center.
  • Royce stamps three animals onto his paper and then writes a backwards 3 on his paper.

Uses math language to express quantity in everyday experiences.

  • Myra tells her friend, “Look, there are two cookies left."
  • While playing outside, Saveem and Crystal count the number of jumps it takes to move from one area to another.
  • Moshe accurately counts each scoop of sunflower seeds she pours into the container.​​

Child identifies, describes, compares, and composes shapes.

​ P-MATH 10.

Child explores the positions of objects in space.

Recognizes and names some basic shapes.

  • While playing Shape Bingo the caregiver calls out “circle". Kenniah points to the circle ​on his game board and uses the game piece to cover it up.
  • When the therapist asks Sammy which hole the square block should go in, Sammy puts the square block in the correct hole.
  • Jeremiah chooses the card with the outline of several different triangles, places playdough along the sides of the large triangle and says, “I'm making triangles."
  • While looking at the screen with several circles, triangles and squares, Alisha points to each shape and says its name.

Describes and compares the characteristics of basic shapes using descriptive and geometric language.

  • When asked what she notices about the triangle, Skylar responds “pointy".
  • “This triangle is tall and this triangle is fat." says Abigail as she moves shapes on the tablet.
  • Wyatt places all of the squares in one group and all of the circles in another group.  When the teacher asks about how he decided to sort the shapes, Wyatt responds, “These are all round.  These are like a box."
  • Samuel says, “The square has four sides. The triangle has three."

Combines and separates 2D and 3D shapes to make other shapes or designs.

  • Shelby adds two rectangular unit blocks and three triangular shaped blocks to the castle he is building in the block center.
  • Ellie selects several shapes and glues them onto her paper, creating a “robot".
  • Eric plays with a friend at the Flannel Board, where two triangles are placed together to make a square.  Eric removes one of the triangles and says, “Now we have a triangle".
  • Looking at a card that shows 4 colored squares arranged to make a rectangle, Angel arranges similar colored squares to duplicate the same rectangle. 
  • After using pattern blocks to create a geometric design, Savannah removes the blocks from the work mat and begins to use the same shapes to make a different design.

Completes simple puzzles.  

  • Cary picks up the last puzzle piece by the knob and places it in the correct space. 
  • Elise completes the five-piece shape puzzle with circle, square, oval, rectangle and triangle shapes.
  • Taylor and Maria take turns putting together 10- and 12-piece interlocking puzzles. 

Identifies the shape of objects in the environment.

  • While playing the I Spy the Shape game, Shayla says, “I see a rectangle. It's the door!"
  • Amanda points to the library window and signs, “square".
  • Julie tears a corner of the construction paper and communicates, “Look! A triangle!"
  • On the playground, Grayson carefully steps onto each square paver saying, “You can only step on the squares. Otherwise, you'll fall into the fire!"

Identifies parts of a whole.

  • When the speech therapist shows Juan a picture board with a variety of photos and asks, “Which of these is part of an apple," Juan points to the apple slice.
  • Curt says, “This piece belongs to the cat puzzle."
  • Shawna tells her caregiver that she needs the top to the paint container.

Demonstrates knowledge of the relative position of objects.

  • Hector puts his hands on his head in response to a movement song.
  • The teacher says, “Show me the one on the bottom," and Damon points to the correct object.
  • When asked, Kayla goes and gets the book that has fallen under the table.
  • After volunteering to be one of the five ducks, Louis stands next to Owen as requested by the teacher. 

Uses words that indicate directionality, order and position of objects.  

  • While singing “Going on a Bear Hunt, Harper mimics the teacher's movement for “over", “under" and “around".
  • After listening to his teacher read Rosie's Walk to the class and being asked to name one place Rosie traveled, Oscar points to cards on his communication board to indicate that Rosie walked under the beehive.
  • Caleb says, “Oh no! The ball went over the fence."
  • Camila looks for the missing puzzle piece, finds it and says, “Found it! It was behind me!"
  • Tran says to Serenity, “I want to go first this time."​​
​ P-MATH 7.

Child understands simple patterns.

Describes objects by one or more attributes.

  • Abigail covers the glue on the paper with sequins and says, “They are so sparkly!"
  • Marco says, “That's a big blue triangle."
  • Aubrey is playing in the block area and tells her friend, “These blocks are red but these ​blocks are blue" as she points to the blocks on one shelf that has red blocks and then another shelf that has blue blocks laying on it.
  • Carter's teacher asks him to describe a picture he is holding up. Carter responds, “The birds have wings and the dogs have legs." 

Matches objects. 

  • Digging through the collection of beads, Edie matches a red bead to an identical red bead and puts them aside.
  • Playing a lotto matching game, RoShonda matches the circle shape object to the picture of the circle shape on the game board.
  • Natalie tosses the beanbag with a photo of a red strawberry pinned to it and it lands on the matching picture of a red strawberry that's taped to the floor.
  • Holding a toy motorcycle figure in one hand, Jaxon reaches into the mystery bag, feels each object and then pulls out the same identical motorcycle figure.

Sorts and classifies objects by one or more attributes.

  • Tamara digs through the collection of differently colored jewels and picks out all of the green jewels.
  • William gathers all of the doll house bedroom furniture and puts them in one room of the doll house, leaving other types of furniture in the other rooms of the doll house.
  • Skylar places all the red stars in a box and all the blue ovals in another box. 
  • Nora sorts a collection of random rocks into three groups: those that are shiny, those that are flat, and those that are bumpy. 
  • Myra places pennies in one cup and nickels in another cup.  “I put all of the silver ones in this cup", Myra says as she points to the cup with the nickels.
  • Holding another seashell, Easton looks at the three groups of shells and decides to place it with the “round" shells. 

Recognizes, duplicates and extends simple repeating patterns.

  • Ashley makes a bracelet using green, red and yellow beads by copying the green, red and yellow bead pattern in a picture.
  • When walking down the hallway, Desiree says, “It's Red, blue, green, Red, blue, green on the floor."
  • Colton picks a pattern card and reads it out loud, “Dog, cat, cat, sheep, Dog, cat, cat, sheep, Dog, cat, cat, sheep."  Colton then picks up a dog figure and places it next to the card to continue the pattern.

Creates original patterns that repeat.

  • When building a zoo in the block center, Chance and Joshua use cubes and blue stones to make a decorative pattern around the outside of the zoo.
  • Using blocks to make a road for his cars, Gregory designs a pattern by repeating square, triangle, rectangle until the path ends.
  • When selected to create the next body movement pattern, Paisley chooses to clap, then tap her nose, then touch her head.  The rest of the class joins in, as Paisley continues to repeat those three movements.
  • When hooking the plastic links together, Lindy creates a color pattern and says to her caregiver, “This is Red, blue, yellow, Red, blue, yellow, Red, blue, yellow."​​
​ P-MATH 8.

Child measures objects by their various attributes using standard and non-standard measurement. Uses differences in ​attributes to make comparisons.

Compares and/or orders objects using attributes of length, weight and size.

  • As Kyle and Chris stand next to each other, Kyle says, “I'm taller!"
  • Placing the two balls next to each other, Juan says, “The green ball is bigger than the blue ball"
  • Alexander puts the shiny rock on one side of the bucket balance and the black rock on the other side of the balance.  The balance tips down and Alexander says, “The black rock is heavier!"
  • Kaisar lines up three crayons on the table, from shortest to longest.
  • Ashanti stacks the nesting rings by size.

Uses tools to explore measurement.

  • Amy pretends to measure the length of her block road with a tape measure.
  • Philip counts the cups of sand it takes to fill the bowl.
  • Jarred places objects on each side of the balance scale, adding and taking off objects to alter the balance of the two sides of the scale.

Explores, compares, and describes length, weight or capacity using nonstandard units.

  • Andre pours water from a small cup to a large cup. 
  • Tamika uses teddy bears to measure the side of a table and signs, “Nine bears long."
  • John places objects on each side of the balance scale and says, “This truck weighs five blocks." 

Shows awareness of simple time concepts. 

  • LaShonda says, “In the morning we get up."
  • Cory says, “At night it gets dark."
  • Kimmy says that she is in school for a long time until Mommy gets off from work.

Demonstrates understanding of the sequence of events and relative length of time associated with some common activities.

  • Angelica says, “After lunch we go outside." 
  • When he arrives, Kyle arranges the pictures on his visual schedule in order to show his activities for the morning.
  • Lucia says, “Tomorrow is our stay home day [Saturday] and I get to watch TV."
  • Angela tells Chaya, “Hurry up! We only have this much time until Clean Up!" indicating a small amount of time with her hands.​

Unmatched Head Start Goals​

 P-MATH 6.

Child understands addition as adding to and understands subtraction as taking​ away from.