Counting and naming numbers
Students learn to count out loud, point to objects one at a time, and write the numbers they see. By the end of this stretch, most can count past twenty without losing track.
This is the year numbers start to mean something. Students learn to count past twenty, match each number to one object, and figure out which group has more. They start adding and taking away with small piles of cubes or fingers. By spring, students can count to 100, name shapes like circles and squares around the house, and solve simple problems like "I have 3 crackers and you give me 2 more."
Students learn to count out loud, point to objects one at a time, and write the numbers they see. By the end of this stretch, most can count past twenty without losing track.
Students figure out which pile has more and which has fewer. They start matching numbers to real groups, like counting five crackers or six crayons, and noticing when two groups are equal.
Students put small groups together and take some away, using fingers, blocks, and drawings. They start to see that 3 and 2 make 5, and that 5 take away 1 leaves 4.
Students name circles, squares, triangles, and cubes, and notice these shapes around the house and classroom. They also compare which object is longer, shorter, heavier, or lighter.
Students take apart numbers like 13 and 17 into a group of ten and some extras. This sets up the place-value thinking they will use for years to come.
Students figure out what a math problem is asking before they start solving it, and keep trying even when it gets hard.
Students learn to think about numbers two ways: pulled away from a story ("I have 3 apples" becomes just "3") and put back into one. This helps them move between a math problem on paper and the real situation it describes.
Students explain why their answer makes sense, using objects or drawings as proof. They also listen to a classmate's thinking and say whether they agree or disagree.
Students use simple math to make sense of everyday situations. They might draw a picture, count objects, or use shapes and numbers to show how something works in real life.
Students learn to pick the right tool for the job, whether that means grabbing a pencil, using a number line, or making a quick estimate instead of calculating by hand.
Students use the right words and careful counting when they talk and work through math problems. This means saying "circle" not "round thing," and checking that numbers add up before moving on.
Students spot patterns and repeating rules in numbers and shapes, then use what they notice to solve problems. For example, seeing that small numbers always combine the same way helps them add without starting from scratch.
Students notice when the same steps keep showing up in different problems. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students figure out what a math problem is asking before they start solving it, and keep trying even when it gets hard. | CT-MATH.MP.K.1 |
| Reason Abstractly | Students learn to think about numbers two ways: pulled away from a story ("I have 3 apples" becomes just "3") and put back into one. This helps them move between a math problem on paper and the real situation it describes. | CT-MATH.MP.K.2 |
| Construct Arguments | Students explain why their answer makes sense, using objects or drawings as proof. They also listen to a classmate's thinking and say whether they agree or disagree. | CT-MATH.MP.K.3 |
| Model with Mathematics | Students use simple math to make sense of everyday situations. They might draw a picture, count objects, or use shapes and numbers to show how something works in real life. | CT-MATH.MP.K.4 |
| Use Tools Strategically | Students learn to pick the right tool for the job, whether that means grabbing a pencil, using a number line, or making a quick estimate instead of calculating by hand. | CT-MATH.MP.K.5 |
| Attend to Precision | Students use the right words and careful counting when they talk and work through math problems. This means saying "circle" not "round thing," and checking that numbers add up before moving on. | CT-MATH.MP.K.6 |
| Use Structure | Students spot patterns and repeating rules in numbers and shapes, then use what they notice to solve problems. For example, seeing that small numbers always combine the same way helps them add without starting from scratch. | CT-MATH.MP.K.7 |
| Express Regularity | Students notice when the same steps keep showing up in different problems. They use that pattern as a shortcut instead of starting from scratch each time. | CT-MATH.MP.K.8 |
Counting and number sense forms the foundation of kindergarten math. Students count objects, compare small groups, and recognize written numbers, building the number habits they use in every math lesson ahead.
Adding and subtracting small numbers, kindergartners solve simple word problems using objects, drawings, or fingers. They figure out how many are left, how many in all, or how many more one group has than another.
Students sort objects into groups and show what they found using a simple picture graph or tally chart. Reading the chart tells them which group has more, fewer, or the same.
Students sort flat shapes like circles and squares and solid shapes like spheres and cubes by describing what they notice: how many sides, whether edges are straight or curved. They also practice measuring basic shapes using simple tools.
Ratio reasoning in kindergarten means noticing when things match up evenly, like sharing 6 crackers equally between 2 friends. Students use that sense of fair sharing to solve simple everyday problems.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Counting and number sense forms the foundation of kindergarten math. Students count objects, compare small groups, and recognize written numbers, building the number habits they use in every math lesson ahead. | CT-MATH.K8.K.1 |
| Operations and Algebraic Thinking | Adding and subtracting small numbers, kindergartners solve simple word problems using objects, drawings, or fingers. They figure out how many are left, how many in all, or how many more one group has than another. | CT-MATH.K8.K.2 |
| Measurement and Data | Students sort objects into groups and show what they found using a simple picture graph or tally chart. Reading the chart tells them which group has more, fewer, or the same. | CT-MATH.K8.K.3 |
| Geometry | Students sort flat shapes like circles and squares and solid shapes like spheres and cubes by describing what they notice: how many sides, whether edges are straight or curved. They also practice measuring basic shapes using simple tools. | CT-MATH.K8.K.4 |
| Ratios and Proportional Relationships | Ratio reasoning in kindergarten means noticing when things match up evenly, like sharing 6 crackers equally between 2 friends. Students use that sense of fair sharing to solve simple everyday problems. | CT-MATH.K8.K.5 |
Connecticut's spring summative math test for grades 3 through 8, aligned to the Connecticut Core Standards for Mathematics.
Students count, write, and compare numbers up to about 20, and many work with numbers up to 100 by ones and tens. They add and subtract small amounts, sort objects, and name basic shapes like circles, squares, and cubes.
Count real things during the day. Count steps to the car, grapes on a plate, or buttons on a shirt. Ask questions like how many are left after eating two, or which pile has more. Five minutes a day builds a strong number sense.
Reversing numbers like 3 or 7 is common at this age and usually fades with practice. Keep writing numbers together on paper, in sand, or with a finger in the air. If reversals are still frequent by the end of first grade, mention it to the teacher.
Start with counting and matching small groups in the fall, then move to writing numbers and comparing groups up to ten. By winter, build to twenty with ten-frames. Spring is for counting to 100 by ones and tens and early addition and subtraction within ten.
Students solve problems within ten using fingers, counters, drawings, or mental pictures. They can act out a story like four apples plus three more, and explain what they did. Quick recall is not expected yet.
One-to-one correspondence past ten, the teen numbers, and understanding that the last number counted tells how many. Comparing groups using the words more, less, and equal also takes longer than it looks. Plan extra small-group time for these.
Point out shapes on signs, food, and toys, and use words like flat, round, corner, and side. Compare objects by asking which is longer, heavier, or holds more. Cooking, sorting laundry, and setting the table all count.
Ready students count to 100, write numbers to 20, and compare two groups to say which has more. They solve simple add and subtract stories within ten and name common shapes. Students still shaky on counting past 20 will need early support next year.