The days of basking in the sun on the beach or binge watching our favorite television shows in our pajamas may be coming to a close, but the satisfaction of helping children learn and grow is about to begin again! One important way to set students up for mathematical success at the beginning of the school year is to focus on concrete, pictorial, and abstract number sense activities that engage students in fun, interactive, hands-on ways.
So What Is Number Sense?
To put it simply, number sense refers to an understanding of numerals and the quantities they represent. A solid number sense foundation ensures that students can not only count, read, and write numerals but also ensures that he or she understands the quantity each number represents. I always focus on number sense at the beginning of the year prior to diving into a study of place value to ensure that I set my students up for mathematical success! My all-in-one First Grade Number Sense Unit covers numbers 1-120, immersing students in differentiated worksheets, hands-on centers (concrete, pictorial, and abstract), and fun crafts that can easily fit into any primary number sense curriculum or be used as a stand-alone curriculum.
CONCRETE-PICTORIAL-ABSTRACT
I've embedded a Concrete-Pictorial-Abstract approach into my First Grade Number Sense Unit to solidify the learning. The Concrete-Pictorial-Abstract method is a 3-stage instructional approach that has been proven to be highly effective in teaching math. During concrete activities, students physically manipulate objects to solve math problems. During pictorial activities, students use pictures to represent objects in order to solve math problems. During abstract activities, students use only numbers and symbols to solve math problems. Students travel along this continuum throughout the unit of study, often revisiting previous stages.
concrete centers for NUmbers 1-20
I like to begin my primary math instruction with one-to-one correspondence for numbers 1-10, then 10-20 using concrete activities that invite students to physically manipulate objects, such as the Button Jars Center, Spider Webs Center, Ice-Cream Scoops Center, or Roll & Build Center. These centers invite students to represent numbers using concrete objects that they can physically count out one at a time. Later, I introduce pictorial and abstract centers.
pictorial worksheets for reading & writing NUmbers 1-20
The No-Prep Differentiated Spotlight on Numbers 1-20 Worksheets can be used as informal assessments of each student's ability to read, write, and represent numbers 1-20. Each Worksheet invites students to either color or draw (depending on the differentiated level) pictures to represent each number, show the number in a ten-frame, identify and circle the correct number, write the number that comes before and after, and practice writing both the number and number word. Level 3 worksheets invite students to create a part-part-whole number bond for each given number between 1-20.
pictorial & abstract worksheets for counting within 20
Once students have a firm grasp on reading and writing numbers within 20, they can move on to worksheets that invite them to practice counting within 20. The differentiated worksheets include both pictorial and abstract approaches to counting within 20.
pictorial & abstract centers for NUmbers 1-20
After students have had concrete practice with number sense centers, I introduce the pictorial centers. The Number Puzzles Center invites students to match the correct number, number word, and picture to complete each 3-piece puzzle while the Melon Match Center invites small groups of students to engage in a concentration-style game to match each number to its ten or twenty-frame. The abstract centers, like the Number Words Center and Count On & Back Center take away the picture supports and give students practice with just the number symbols.
reading, writing, and representing numbers to 100
After students have a firm grasp on numbers 1-20, I move on to differentiated worksheets that give students practice reading, writing, and representing numbers to 100. These worksheets give students practice coloring, circling, or drawing base ten blocks (depending on the level), coloring a hundreds chart to the correct number, counting on from the number, and writing the number in words.
Counting to 120
Once students have a firm grasp on reading, writing , and representing numbers to 100, I move on to counting within 120. The Common Core requires first graders to be able to count to 120, starting with any number less than 120. These differentiated worksheets offer a variety of fun formats to cover this part of the standard.
pictorial & abstract centers for NUmbers 1-120
I've also included hands-on, interactive centers to give students practice reading, writing, representing, and counting numbers to 120. The Race to 120 game is a fun twist on an old favorite with special rules for landing on desert plants or animals. The Ocean Number Fun Center invites students to select number line strips, then identify and write the missing numbers, and the Guess Who Center includes 2 versions to help students identify missing numbers on 120 charts.
3 LEVELS OF Differentiation
Each worksheet in the Number Sense Unit is differentiated into 3 levels to meet each student as his or her current level of understanding. In the example of the worksheet below, you can see that the Level 1 worksheets offers multiple choice answers for students who need extra scaffolding. Providing choice builds confidence and limits the possibilities for the student. The Level 2 worksheet invites students to write their answers on the blank lines, allowing for an unlimited number of answers and requiring the student to form their numbers correctly. The Level 3 Worksheet provides students with the opportunity to create their own insects inside the jars and write the number on the blank lines. One option is to print Level 2 and 3 front-to-back so that proficient students have a challenge activity when they finish the worksheet.
aligned to the common core
Each Worksheet in my First Grade Math Units is specifically designed to teach a specific Common Core Math Standard. The standard is listed in the top right-hand corner so you know exactly what's being covered. This allows for easy integration into any curriculum. In the case of my Number Sense Unit, each worksheet is aligned to CCSS.MATH.CONTENT.1.NBT.A.1: 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. The rest of the standards in the Number & Operations in Base Ten Domain are addressed in my First Grade Place Value Unit.
I hope some of these ideas have inspired you to implement a Concrete-Pictorial-Abstract approach in your math class this year. You can purchase this all-in-one First Grade Number Sense Unit on my Teachers pay Teachers store.
As a fun, themed spiral review option, I have also created Halloween Themed Number Sense Centers for the month of October that will have your students screaming for more!
what teachers are saying
- This is the best thing I have ever bought on TPT and I have been a customer for years. Thank you! This is perfect! This pack offers so much!
- Great resource to use with my Grade 2 students who need to develop a stronger number sense!
- One of the best purchases I made! It gave reinforce activities to go along with the concepts being taught! Thank you
- WOW! These are so thorough. I LOVE your differentiation method!! This will make my life so much easier! THANK YOU!!