Math

About

Mission: The Elementary Mathematics Vision is for all students to demonstrate mathematical confidence through engaging, hands-on learning experiences.

Vision: We are committed to differentiated instruction based on assessment data, ensuring that all learners develop deep conceptual understanding, fluency, and mathematical proficiency. By fostering a love for mathematics and encouraging active participation, we empower students to apply their knowledge to real-world situations with confidence and purpose.

The CCPS Elementary Mathematics Curriculum standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a+b)(x+y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task, such as expanding (a+b+c)(x+y). Mathematical understanding and procedural skill are equally important, and both are emphasized in the CCPS Elementary Mathematics Curriculum.

Mathematics Grade Level Summer Calendars

Benchmarks

CCPS Elementary Mathematics State Report Card

Students enrolled in Carroll County Public Schools will take 2 county curriculum benchmark assessments. The first is given in January and the second at the end of May. These assessments are aligned with the county curriculum that reflects the standards Maryland College and Career Readiness Blueprint. Students in grades 3, 4, and 5 will also take the Maryland Comprehensive Assessment Program assessment in the spring.

Basic Facts

Elementary Basic Facts by Grade Level
Our goal has shifted from memorizing facts and procedures to increased understanding of the math strategies. We will support student thinking by helping them see when certain strategies are applicable. We begin with building the understanding of each strategy and then move to targeted practice while monitoring progress. The key is to help students see the possibilities and then help them chose the strategy that helps them get to the answer without counting. Meaningful practice of strategies is a key part of developing fact fluency.

Fact Fluency Rationale and Background Document

Overview

To Master Basic Math Facts: Strategize, Then Memorize
by Rinke and McAdam

Nothing may be more feared in the minds of young children and their parents than learning the basic math facts. Just hearing the times tables takes many of us back to our own childhoods, staring at a blank page and trying to remember the dreaded 9 x 8 = 72. The good news is that our own children should not have to suffer the same fear. A substantial amount of mathematics education research shows that children do not master their math facts through memorization alone. Instead, true mastery comes from being equipped with quick and effective strategies for finding the solution. By using these strategies, children will always have the mental tools needed to find the correct answer and the confidence to use them.

With a strategy-based approach to the basic math facts, children use what they already know to figure out what they don’t know. Rather than racking their brains to remember the answer to a basic math fact, they can simply find a “helping” fact and use it as a jumping- off point. For example, let’s say that your child knows the common fact 5 x 5 = 25. She can then add one more 5 to figure out that 6 x 5 = 30. Think of this as the “one more than” strategy. There are many such strategies that parents can teach their children in order to equip them with the tools they need to master all of their math facts. As a parent, remember that as long as your child can figure out an answer quickly in her head (in about 3 seconds or less), she has mastered the fact and can use it in meaningful ways as part of her daily life.

Kindergarten

First Grade

Strategy Focus in First Grade

Doubles
Halves
Make ten
Subtract from ten
Count on 2
Count back 2

Instructional Guide

Instructional Guide

Subtraction Fact Cards

Think Addition

Second Grade

Third Grade

Strategy Focus in Third Grade

Skip counting
Doubles
Powers of 10
Properties
Double double
Add another set
Double double double

Quarter Information

Quarter 1

Foundations Facts
Multiplication
Division

Quarter 2

Building on Foundation Facts
Multiplication
Division

Quarter 3

Building on Foundation Facts
Multiplication
Division

Quarter 4

All:
Multiplication and Division

Resources

Phases of Learning

Modeling Phase: Modeling and/or counting all or counting on to find the answer: For example, using fingers to help keep track of their counts to solve 5+7=?
Reasoning Phase: Deriving answers using reasoning strategies based on known facts, such a solving 5+7 by thinking, “Five plus five equals ten, and two more will make twelve.”
Efficient Phase: Mastery or efficient production of answers. For example, when asked, “What is 5 + 7?” a child might call out, “Twelve,” and explain, “I just knew it.”