- A Parent’s Guide to the 1st Grade Math Common Core - February 13, 2013
- A Parent’s Guide to the Kindergarten Math Common Core - January 29, 2013
- First in Math and Reflex Math: A Program Comparison - November 5, 2012
- Procedures versus Concepts: A Mathematical Dilemma - October 18, 2012
- The Mathematical Workshop Model: How Data, Differentiation, and Classroom Management Combine in an Elementary Classroom - October 12, 2012
So your precious Kindergarten student has successfully graduated and moving on to First Grade. They can count to 100, fluently add and subtract within 10, and even identify many geometric shapes. However, now they are in First Grade. That Kindergarten year sure did go by quickly! Here is what your now 1st grade student can expect to learn in math and what you can do to help prepare them.
The Counting and Cardinality domain no longer exists. That domain is only for Kindergarten. But don’t worry; there are not any new domains you need to learn about – not until Third Grade.
There are four major domains in First Grade: Operations and Algebraic Thinking, Number and Operations in Base Ten, Measurement and Data, and Geometry. These are the same domains from Kindergarten minus the Counting and Cardinality domain. All four of these domains build upon what your kindergartner learned last year. If you notice your student having any difficulty in basic counting or addition, these are things you can work on with your First Grader over the summer. Take a peek at my last article: A Parent’s Guide to the Kindergarten Math Common Core to review what your student should have mastered before entering First Grade.
To begin with, your First Grader now will be asked to add and subtract fluently within 20. This builds upon their ability to already be able to add and subtract fluently within 10. Ask your student what happens when you add. See if they can tell you that numbers get bigger. Conversely, a First Grade student should tell you than when we subtract, numbers get smaller. A great manipulative to use to help understand this concept are Unifix cubes. Students can visually see and physically create an addition problem that demonstrate a larger number of cubes connecting when we add, a smaller number of cubes being left when we subtract or break apart those Unifix cubes.
Try to put these ideas in real world concepts for your student. They will be asked to use addition and subtraction within 20 to solve world problems as well. So it is important that they are not only seeing naked numbers (i.e., 12 + 3), but that they also understand these ideas in everyday life. For example, while unpacking groceries, ask your student to count how many cans of soup you bought. Were there already some soup cans in the cabinet? How many do we have now? It is important to be involved in this process with your student as much as possible, especially at a younger age. Students’ attitudes towards mathematics are one of the strongest indicators of their success. Your willingness to work with them in a fun and engaging way is one of the best ways to build a positive attitude towards math and school in general.
Next, but still within the same domain, students need to understand the meaning of the equals sign. It is imperative that parents as well as teachers demonstrate and explain that the equals sign simply means “the same as” and not “the answer is coming up on the right side of the equal sign.” For example, a students should be able to write and explain: 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, and 4 + 3 = 5 + 2. These ideas are part of the Operations and Algebraic Thinking domain, not because First Grade students will be computing Algebra of course, but rather we are laying the foundation for their conceptual understanding when they begin to solve algebraic equations and expressions in the upper grades.
Moving to the Number and Operations in Base Ten domain, students will now be asked to count to 120. They will be asked to do so starting from any number. That is, instead of simply counting with your student from one, start at 56, 89, or 101, and see if your student can count successfully from there. First grade students should be able to read, write and represent these numbers as well. A great way to build upon these concepts is through estimation. Although First Grade students will not be asked yet to estimate formally, to understand just how much 100 is, ask your student how many M&Ms they think are in a bag. Spread some toothpicks out on the table and ask your student to estimate how many there are and then actually count them. You can do very similar activities with beans, paperclips, pencils, etc.
One other very important concept under this domain is for students to begin to understand the tens place value. They should be able to explain that 10, is simply a “bundle” of ten ones. When students begin adding and subtracting within 100 (through 20 is what they expected to do fluently), it is very important for teachers (and parents when helping with homework) that they say the appropriate place value when stating numbers. For example, if you ask a student what 14 + 2 is and you are solving it on paper, we usually start off by stating, “what is 4 + 2” (using the ones place first), and then “one plus nothing is one, so bring down the one.” However, that is not, in fact, a one. It is a ten. The appropriate way to say that is “ten plus nothing is ten.” Since we already have a six in the ones place, ten plus six is sixteen. Intermediate students often struggle with basic place-value and using this strategy will help reinforce the idea of place value as students navigate through these concepts. First grade students should be able to explain a bundle of ten ones (10), two tens (20), three tens (30), etc., until they reach 90. They will be asked to mentally “add ten” to any given number. By reinforcing these concepts, this should become a simple task because students will begin to master the tens place value.
In the Measurement and Data domain, First Grade students will be asked to order objects by length and compare the length of at least two objects. They began this concept by understanding length and weight in Kindergarten. Students will be asked to count by basic units to measure an object. For example, back to our Unifix cubes, students should be able to lay cubes against and object from end to end and explain, “This stapler is 7 cubes long.” This will begin to prepare students for the use of a ruler. Students can then compare the length of this stapler to the length of their desk and explain which one is longer or shorter and why.
Also found in this domain is telling and writing time. First grade students will be asked to tell and write time in hours and half-hours using analog and digital clocks. This is a great time to get your first grader their first watch! Whenever you are wondering yourself what time it is, ask your first grader. Have both an analog and digital clock available in your house. When driving in the car, ask your student to tell you the time displayed. Instead of saying “the big hand and little hand,” begin saying “the hour hand and the minute hand.”
Finally, we come to the Geometry domain. In Kindergarten, students were asked to describe the spatial awareness of shapes (above, below, next to, below, etc.). Expanding on these concepts, First Grade students will be asked to create two-dimensional shapes: rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles or three-dimensional shapes: cubes, right rectangular prisms, right circular cones, and right circular cylinders, to create composite shapes (larger shapes that contain smaller shapes). This sounds much more difficult than it actually is. Students will not be asked to identify a “right rectangular prism.” In First Grade these are simply the names of the objects teachers will use when asking students to create a larger shape out of smaller shapes (composite shapes). Teachers generally use tessellations while teaching this concept. However, students should be able to begin discriminating between objects such as triangles and squares by understanding that triangles have three sides and squares have four. Specific terms First Graders will have to say and be able to use within this domain are: halves, fourths, and quarters. They will do so by partitioning circles and rectangles into these subsequent parts. This is an excellent opportunity to make a connection back to telling time so that a student can begin to understand why an adult may say the time is “half-past seven” rather than 7:30, or “a quarter-after nine” rather than 9:15.
A simple way to help your student at home with Geometry is to ask them to identify shapes around your home. Is your television a rectangle or square? How do you know? Is that ice cream cone you got from McDonald’s really a cone? Does is have that single vertex (corner/point) at the bottom of that cone? Those soup cans we were counting earlier – what shape are those? How much water is left in my glass – half? A quarter? There are plenty of possibilities here, the most important being that as a parent you are simply engaged in making this learning fun for your student.
As a parent, do not be afraid to ask your teacher for clarity on any of these standards and to provide more ways at home to assist your student. Many teachers across the country have yet to begin teaching the Common Core standards and will be learning this right along with you. Partner with your child’s teacher and remember that open communication is imperative for your child’s success.
Stay tuned for my next article: A Parent’s Guide to the 2nd Grade Common Core.