Pre-assessment Differentiation in Teaching First Grade Math
In a first grade classroom, 22 students were given a pre-assement at the beginning of the second week of school in order to determine where they fell in their understanding of Math concept standards. According to the California C.O.R.E. standards, by the time students enter into the first grade they should already have a solid understanding of the following math concepts:
1. Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as
counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining
and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten
students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged,
but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions,
including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting
the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.
(2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary.
They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and
hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes
such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their
environment and to construct more complex shapes.
- California
Common Core
State Standards 2013
I presented students with a baseline preassessment in order to gauge the following skills: addition and subtraction with double digit numbers, writing numbers 1 -25, and filling out a number chart 1 - 120. After students completed the First Grade Math Preassessment, I was able to gauge their knowledge and understanding in accordance with the above CORE standards and the following results were presented:
- 5 students answered the most questions correctly, including the most difficult of the pre-assessment questions.
- 12 of the students demonstrated having some knowledge of Math Common Core Standards, but need to develop higher order thinking skills
- 5 students appear to have limited knowledge of Math Common Core Standards. Three of those students show signs that they are struggling with language and are at different reading levels, and 2 students show little to no comprehension of the Math Common Core Standards and therefore need to be tested further for special needs
Based off of the information gathered on student performance provided by the results of the pre-assessment, students will be placed into the following 3 groups and both their instructional lesson time as well as their further assessments will be tailored to meet their academic needs. Students will all begin working on the Math concepts of addition and subtraction and place value of numbers.
Tier 3: Above Grade Level
Differentiated Instruction:
The 5 students who displayed having a firm grasp on California Common Core Math Standards and who were able to answer the most questions correctly, including the most difficult of the pre-assessment questions, will move forward in the subject material by deepening the understanding of math concepts.
ADDITION AND SUBTRACTION
Students will work on computer programs and in small groups where they will begin focusing on representing and solving problems involving addition and subtraction with three numbers (into the 100's), to solve one and two step word problems as well learning about the relationship between addition and subtraction up to the number 20.
ex activity: Represent And Solve Problems Involving Addition And Subtraction.
PLACE VALUE
Students will take what they have learned about place value and through the use of their knowledge of base 10, work to begin to understand concepts of greater than and less than by Comparing Numbers.
Differentiated Assessment:
As these students move through each new element, they will be assessed at the end of each lesson on their understanding and comprehension of the newly learned skills through teacher led games and activities in the classroom and through computer based end of lesson assessments or "quizzes".
Tier 2: At Grade Level
Differentiated Instruction:
The 12 students who demonstrated having some knowledge of Math Common Core Standards, but need to develop higher order thinking skills will continue with the established 1st grade math curriculum. Students will go through a brief period of reviewing what they learned year before in kindergarten in order to further deepen and refresh their level of understanding and comprehension and then begin learning new related concepts.
Through teacher led games and activities as well as through computer based assessment programs, students will review their understanding and comprehension of addition and subtraction and place value concepts and then demonstrate their learning by completing a computer based learning activity, worksheet or teacher led lesson or activity:
PLACE VALUE
1. Students will begin to learn about place value and will use place value understanding and properties of operations to add and subtract. Students will be taught that the two digits of a two-digit number represent amounts of tens and ones. First graders will learn the tens and ones place values through online learning games and classroom activities like Roll and Build and will learn correct mathematical terminology (ie: Saying 67 as "6 tens, 7 ones" as well as "sixty-seven" ).
1. Students will begin to learn about place value and will use place value understanding and properties of operations to add and subtract. Students will be taught that the two digits of a two-digit number represent amounts of tens and ones. First graders will learn the tens and ones place values through online learning games and classroom activities like Roll and Build and will learn correct mathematical terminology (ie: Saying 67 as "6 tens, 7 ones" as well as "sixty-seven" ).
ADDITION AND SUBTRACTION
Students will work on addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing :Addition and Subtraction word problems
Students will work on addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing :Addition and Subtraction word problems
Differentiated Assessment
Tier 3: Below Grade Level
Differentiated Instruction
The remaining 5 students who appear to have limited knowledge of Math Common Core Standards will be grouped together, but the material that is presented to them will differ in context of materials and presentation, depending on student's specific needs: ELL and special needs.
For these students, all 5 will be retaught what they were introduced to in kindergarten, but the information will be scaffolded in such a way that each student will move onto learning a new skill once an initial skill is mastered.
1. Lessons for struggling students will be scaffolded beginning with material introduced to them in kindergarten. Students will work on using manipulatives to compose and decompose numbers from 11-19, in order to understand what sum 11-19 represent ( For example, a number such as 15 looks like the numbers "one" and "five", not 1 ten and 6 ones). An example of some activities using manipulatives to make groups of tens and ones could be as follows:
ADDITION AND SUBTRACTION
1. Students will revisit and practice Choral counting from 1-120 forwards and backwards starting with sequence counting from 1-30 and then over time increasing from 1-50 and then 1-100. Students will also solve simple addition and subtraction problems either through teacher led mental math imagery stories with the aide of manipulatives or using computer based math games or worksheets with the aide of objects or drawings to represent the problem.
Mental math activity using maipulatives (students count out gems and take them away according to the story):
"Chatter the red squirrel was out collecting acorns for the winter and as he was scurrying about he picked up three acorns and put them into his pouch. (students take 3 gems and put them in front of them). As he was hopping up the tree one gems fell out of his pouch. How many gems did Chatter have now?......."
Example activity of learning numbers past 10:
Students revisit what "teens' are using the following activity Grouping Numbers into teens
ELL and Special Ed Modifications:
The following modifications will be implemented into the instruction given to students who are ELL or have special needs: the language used to describe tasks will be simplified, there will be periodic check-ins with students to track their understanding and comprehension of material taught, pictorial representations will be provided to students along with words when possible in order to provide a clearer understanding of material presented.
The following modifications will be implemented into the instruction given to students who are ELL or have special needs: the language used to describe tasks will be simplified, there will be periodic check-ins with students to track their understanding and comprehension of material taught, pictorial representations will be provided to students along with words when possible in order to provide a clearer understanding of material presented.
Differentiated Assessment
Here is a visual representation of process of differentiating the math lesson for first graders:First Grade Math
References:
California Department of Education. (n.d.) Common Core State Standards
https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf
Differentiation & LR Information for SAS Teachers.Differentiation. Pre-Assessment ideas. Retrieved from the internet on December 5th, 2019. https://sites.google.com/site/lrtsas/differentiation/5-preassessment-ideas
Illustrative Mathematics. Retrieved from the internet on Dec 5, 2019. 1.OA At the Park
https://s3.amazonaws.com/illustrativemathematics/attachments/000/008/571/original/public_task_160.pdf?1462387606
Illustrative Mathematics. Retrieved from the internet on Dec 5, 2019. 1.NBT Roll & Build.
https://s3.amazonaws.com/illustrativemathematics/attachments/000/009/053/original/public_task_987.pdf?1462394355
Illustrative Mathematcis. Retrieved from the internet on Dec 3, 2019. 2.OA A Pencil and a Sticker https://s3.amazonaws.com/illustrativemathematics/attachments/000/008/463/original/public_task_1.pdf?1462386937
Teacher Pay Teachers. Retrieved from the internet on Dec 2, 2019. Kindergarten Addition & Subtraction Assessment. https://www.teacherspayteachers.com/Product/Kindergarten-Addition-Subtraction-Assessment-1176272
https://s3.amazonaws.com/illustrativemathematics/attachments/000/009/053/original/public_task_987.pdf?1462394355
Illustrative Mathematcis. Retrieved from the internet on Dec 3, 2019. 2.OA A Pencil and a Sticker https://s3.amazonaws.com/illustrativemathematics/attachments/000/008/463/original/public_task_1.pdf?1462386937
Teacher Pay Teachers. Retrieved from the internet on Dec 2, 2019. Kindergarten Addition & Subtraction Assessment. https://www.teacherspayteachers.com/Product/Kindergarten-Addition-Subtraction-Assessment-1176272
g and building upon the student’s current knowledge. Use the resources provided on the next slide to help with differentiating instruction, tasks, and assessments. Consider prerequisite skills that are missing for some students and differentiate the learning for them. Consider addressing misunderstandings that students have. Consider extending and building upon the student’s current knowledge. Use the resources provided on the next slide to help with differentiating instruction, tasks, and assessments.
