Counting and number names
Students learn to say numbers in order, count groups of objects, and write numbers on the page. By the end of this stretch, counting to twenty feels familiar.
This is the year numbers start to mean something. Students learn to count past twenty, match a number to a pile of objects, and figure out which group has more. They begin adding and taking away with small numbers, often using fingers, blocks, or pictures. By spring, students can count to 100, name common shapes like circles and squares, and solve simple problems like four apples plus two more.
Students learn to say numbers in order, count groups of objects, and write numbers on the page. By the end of this stretch, counting to twenty feels familiar.
Students decide which pile has more, which has less, and which are equal. They start using fingers, cubes, and drawings to show their thinking.
Students put small groups together and take some away, working with numbers up to ten. Expect a lot of counting on fingers and drawing dots, which is exactly how this skill starts.
Students name circles, squares, triangles, and rectangles, then notice the same shapes on signs, buildings, and toys. They also sort objects by size, color, and shape.
Students compare how tall, how long, and how heavy things are using everyday objects. They also start reading simple picture graphs to answer questions about a group.
Students learn to figure out what a math problem is asking before they start solving it, and to keep trying even when the answer isn't obvious right away.
Students move back and forth between a real situation and the numbers that describe it. They might turn "3 apples and 2 more" into the number 5, then explain what that 5 actually means.
Students explain why their answer makes sense and listen to how classmates solved the same problem. They practice agreeing, disagreeing, and asking questions about each other's thinking.
Students use drawings, objects, or simple number sentences to make sense of real-life situations, like figuring out how many apples are left after sharing some.
Students learn to pick the right tool for the job, whether that means using a pencil, a calculator, or just making a quick estimate in their head.
Students use the right words when talking about math and check that their answers make sense. In kindergarten, that means saying "more" or "less" correctly, naming shapes by their real names, and counting carefully so nothing gets skipped.
Students notice patterns and shapes that repeat or fit together, then use what they see to solve a problem. A child spotting that all squares have four equal sides is using this skill.
Students notice when the same steps keep working the same way and use that pattern as a shortcut. For example, if adding zero never changes a number, they start expecting that instead of rechecking every time.
| Standard | Definition | Code |
|---|---|---|
| Make Sense of Problems | Students learn to figure out what a math problem is asking before they start solving it, and to keep trying even when the answer isn't obvious right away. | NJ-MATH.MP.K.1 |
| Reason Abstractly | Students move back and forth between a real situation and the numbers that describe it. They might turn "3 apples and 2 more" into the number 5, then explain what that 5 actually means. | NJ-MATH.MP.K.2 |
| Construct Arguments | Students explain why their answer makes sense and listen to how classmates solved the same problem. They practice agreeing, disagreeing, and asking questions about each other's thinking. | NJ-MATH.MP.K.3 |
| Model with Mathematics | Students use drawings, objects, or simple number sentences to make sense of real-life situations, like figuring out how many apples are left after sharing some. | NJ-MATH.MP.K.4 |
| Use Tools Strategically | Students learn to pick the right tool for the job, whether that means using a pencil, a calculator, or just making a quick estimate in their head. | NJ-MATH.MP.K.5 |
| Attend to Precision | Students use the right words when talking about math and check that their answers make sense. In kindergarten, that means saying "more" or "less" correctly, naming shapes by their real names, and counting carefully so nothing gets skipped. | NJ-MATH.MP.K.6 |
| Use Structure | Students notice patterns and shapes that repeat or fit together, then use what they see to solve a problem. A child spotting that all squares have four equal sides is using this skill. | NJ-MATH.MP.K.7 |
| Express Regularity | Students notice when the same steps keep working the same way and use that pattern as a shortcut. For example, if adding zero never changes a number, they start expecting that instead of rechecking every time. | NJ-MATH.MP.K.8 |
Counting and number work in kindergarten means learning to count objects, say numbers in order, and understand that each number means a specific amount. Students work with whole numbers to build the foundation for all later math.
Adding and subtracting small numbers to solve simple word problems. Students use objects, drawings, or equations to show how things come together or get taken apart.
Students sort real objects into groups and count how many are in each group. Then they show what they found using a simple picture or tally chart.
Students sort and describe flat and solid shapes by their sides, corners, and size. They learn to tell the difference between a square and a cube, a circle and a sphere.
Students use ratio reasoning to solve everyday problems at the Kindergarten level. This might mean comparing groups of objects to see which has more, or figuring out how things relate to each other in simple, concrete situations.
| Standard | Definition | Code |
|---|---|---|
| Counting and Number | Counting and number work in kindergarten means learning to count objects, say numbers in order, and understand that each number means a specific amount. Students work with whole numbers to build the foundation for all later math. | NJ-MATH.K8.K.1 |
| Operations and Algebraic Thinking | Adding and subtracting small numbers to solve simple word problems. Students use objects, drawings, or equations to show how things come together or get taken apart. | NJ-MATH.K8.K.2 |
| Measurement and Data | Students sort real objects into groups and count how many are in each group. Then they show what they found using a simple picture or tally chart. | NJ-MATH.K8.K.3 |
| Geometry | Students sort and describe flat and solid shapes by their sides, corners, and size. They learn to tell the difference between a square and a cube, a circle and a sphere. | NJ-MATH.K8.K.4 |
| Ratios and Proportional Relationships | Students use ratio reasoning to solve everyday problems at the Kindergarten level. This might mean comparing groups of objects to see which has more, or figuring out how things relate to each other in simple, concrete situations. | NJ-MATH.K8.K.5 |
New Jersey's spring summative math test for grades 3 through 9, aligned to the NJ Student Learning Standards for Math.
Most students count to 100, count groups of objects up to 20, and write numbers from 0 to 20. They also add and subtract small amounts up to 10, compare which group has more, and name basic shapes like circles, squares, and triangles.
Count real things during the day: stairs going up, grapes in a bowl, socks coming out of the dryer. Ask questions like how many are there and how many would be left if we took two away. Five minutes a day matters more than a long session once a week.
Hand them something to count with, like pennies, beans, or crackers. Reading the problem out loud and acting it out with objects almost always helps. Getting a wrong answer is fine as long as students keep trying.
Spend the first months on counting, one-to-one matching, and writing numbers to 10. Move into comparing groups and shapes by midyear. Save addition and subtraction within 10, and counting past 20, for the second half once number sense is solid.
Writing numbers without reversals, counting past 13 without skipping, and recognizing that the last number said tells how many. Teen numbers are the hardest spot because the words do not match the place value pattern. Plan extra practice there.
No memorization is expected yet. Students should be able to figure out sums and differences within 10 using fingers, objects, or drawings. Quick recall of pairs that make 5 and 10 is a nice bonus but not required.
Students name flat shapes like squares and circles and solid shapes like cubes and cones. They also compare two objects directly, asking which is longer, shorter, or heavier. Sorting buttons or toys by size and shape at home counts as real practice.
Ready students count to 100 by ones and tens, count out a group of 15 accurately, and solve simple add-and-subtract stories within 10. They can also compare two written numbers up to 10 and explain their thinking with objects or pictures.