First Grade Math Common Core State Standards and Curriculum
The United States education system includes 3 main levels: primary, secondary, and higher.
The primary school in the United States begins around the age of 5, when children go to elementary school, and continues for 6–7 years. Typically, children finish elementary school at the age of 11-12.
Throughout these years, the main disciplines are taught by one teacher. The exceptions are music, drawing, and physical education. Arithmetics (math), reading and writing are taught to everyone while natural and social sciences are not common.
Mathematics is one of the compulsory subjects from first grade until the end of the school, so let’s consider the curriculum and common core math standards grade 1 children will face.
Math classes form the children’s development in the basic logical operations (classification, generalization, analysis), form an idea of geometric shapes and shape of objects, as well as their position in space.
Of course, there are generally accepted rules and instructions, but each school and teacher adjust the curriculum for themselves and their class. Some people prefer to use pictures as an explanation, others prefer life situations, illustrative examples using specific materials (coins, diagrams). The training system is different, but one way or another, the plan remains unchanged.
Number Sense and Operations
In such classes, children learn to add and subtract. This is the basis of mathematics and the most important thing that needs to be learned.
Basic skills the children need to learn:
- forming simple mathematical representations;
- knowing the name and sequence of numbers from 1 to 100 and learning to write and compare them;
- counting to 100;
- being able to add and subtract;
- learning to read examples, equalities, and inequalities correctly;
- knowing the concepts of left, right, above, below, closer, further, close, far, near, high, low, deep;
- comparing items, making pairs;
- solving equations of the type a ± x = b; x ± a = b;
- solving simple tasks in two actions ("increase by ...", "decrease by ...");
- comparing difference;
- learning to hatch and colorize, draw dots, patterns, straight, inclined and broken lines.
General first grade math standard simply that the children will learn to think logically, analyze and build simple algorithms:
- comparing numbers;
- distinguishing equal signs and inequalities +, -, =,>, < (less, more and equal) and using them correctly;
- solving tasks with one unknown;
- studying and comparing monetary values (25, 50 and 100 cents);
- being able to classify objects (by color, shape, size, purpose, material) and distribute them based on general differences;
- inventing tasks according to drawings and solving them with visual material;
- finding an item in a group of items that “doesn’t belong”;
- solving creative tasks;
- developing logical abilities.
Geometry and Spatial Sense
According to 1st grade common core math standards,pupils continue to study two-dimensional and three-dimensional figures that they know from kindergarten.
First-grades should know how to:
- recognize and name flat geometric figures: triangle, quadrangle, pentagon, hexagon, polygon, trapezoid, circle, oval, semicircles and quarters;
- build and draw shapes;
- classify figures according to signs (shape, size, color);
- determine their position among surrounding objects, learn the concepts of inside and outside, use prepositions: in, on, above, under, behind, in front, between, from, to, through;
- sort figures by vertices, edges and the number of sides;
- use counting sticks to fold geometric figures, numbers, letters, objects;
- recognize geometric shapes: point, straight line, ray, open curve, closed curve, broken line;
- compose an integer from parts;
- add missing elements;
- combine shapes and create others;
- understand directions: from left to right, from right to left, from top to bottom, from bottom to top, forward, backward, in the same direction, in the opposite direction.
- find geometric shapes in real situations;
- divide circles and rectangles into two and four identical parts, describe them using halves, quarters.
This aspect is very important. CCSS math 1st grade considers that the child needs to:
- use measurement units of length, volume, and mass ( centimeter, decimeter, liter, kilogram);
- compare and arrange objects according to their length and weight;
- study temperature, time, and money. Understand the work of watches, calendars, and thermometers;
- calculate the length of an object by placing its smaller copies inside;
- determine the length of figures and objects;
- actively use the words: large, small, larger, smaller, the same size, longer, shorter, equal in length, higher, lower, the same in height, narrower, wider, identical in width, thicker, thinner, uniform in thickness, lighter, heavier, equal in weight, identical and different in form, the same and different in color;
- write the time in hours and minutes using the clock;
- understand what “more” and “less” is.
Data Analysis and Probability
First-graders must learn to analyze and answer simple questions choosing from several options. With CCSS math grade 1 pupil swill learn how to:
- distinguish defining attributes (color, orientation, total size);
- distinguish between parts of the day: morning, day, evening, night;
- give answers based on known factors;
- discuss results and actions with different variables;
- compose questions and analyze results;
- analyze chart data;
- make predictions using this information/find logical connections and patterns;
- continue a logical series of objects;
- form the ability to analyze, compare, generalize, group;
- compare and contrast.
In addition to mathematical knowledge, the child will also gain some skills that will help them to communicate in the future:
- learn about communication and behavior in public places;
- develop the basic mental functions necessary for learning (attention, memory, thinking);
- form educational motivation;
- develop hearing, motor skills;
- creatively develop as a person,
- participate in collective conversations;
- use accepted norms of polite speech communication.
- develop communication skills and social skills.
First Grade Math Curriculum and Standards Summary
To make the educational process joyful and exciting, it is better to implement game tasks, colorful books, and interesting exercises. The main principle of teaching children is learning by playing. Teaching children with the help of fascinating books helps to gradually develop the joy of playing into the joy of learning.
Riddles, counters, puzzles, entertaining problems of mathematical content can be used in the classroom.
What else can be done to entertain the children and make their study time more simple and interesting? ArgoPrep
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Additional Resources Related to First Grade Math
If you’re interested in the first grade math, you might also be interested in our other first grade subject workbooks:
- Letter Tracing Workbook for Preschoolers.Learn to trace letters and words and develop fine motor skills!
- Number Tracing Workbook for Preschoolers.Learn to trace numbers and develop hand-eye coordination!
- Cursive Handwriting Practice Workbook for Pre-K to 5th Grade.Learning cursive writing offers many benefits to children, including increased creativity.
- Shape Tracing and Coloring Practice Workbook for Preschoolers to 3rd Grade.Learn to trace simple and complex shapes.
- Sight Words Practice Workbook for Preschoolers.This workbook teaches your kid to recognize, read and write the sight words.
- Kids Word Search for Preschoolers.Word Search for Kids by ArgoPrep is a fun puzzle workbook that helps your kid build vocabulary and increase word recognition.
Operations & Algebraic Thinking
Represent and solve problems involving addition and subtraction.
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Understand and apply properties of operations and the relationship between addition and subtraction.
Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
Add and subtract within 20.
Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Work with addition and subtraction equations.
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.
Number & Operations in Base Ten
Extend the counting sequence.
Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
Understand place value.
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
10 can be thought of as a bundle of ten ones — called a "ten."
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
Use place value understanding and properties of operations to add and subtract.
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Measurement & Data
Measure lengths indirectly and by iterating length units.
Order three objects by length; compare the lengths of two objects indirectly by using a third object.
Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
Tell and write time.
Tell and write time in hours and half-hours using analog and digital clocks.
Represent and interpret data.
Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
Reason with shapes and their attributes.
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
Compose 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 a composite shape, and compose new shapes from the composite shape.1
Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.