K8 Critical Areas of Focus
The Ohio
Learning Standards for Mathematics include critical areas
for instruction for each grade, K8. The critical
areas are designed to bring focus to the standards
at each grade by describing the big ideas that educators
can use to build their curriculum and to guide instruction. The gradelevel introductions include at least two and no
more than four critical areas for each grade.
The purpose of K8
Critical Areas of Focus is to facilitate discussion among teachers and curriculum experts
and to encourage coherence
in the sequence, pacing, and units of
study for gradelevel curricula.
Standards Revision and Next Steps
In the fall, the proposed revisions to the Ohio Learning Standards for Mathematics and English Language Arts will be shared with the State Board of Education. These proposed revisions are eligible to be approved by the State Board sometime this winter.
Following State Board approval, the department will be updating the Model Curriculum for Mathematics and English Language Arts. A link with information on how to provide suggestions for updates to the Model Curriculum will be coming in the future.
Model Curriculum
The purpose of Ohio’s model curriculum is
to provide clarity to the standards, the foundation for aligned assessments,
and guidelines to assist educators in implementing the standards.
Every grade level or conceptual category in the model curriculum contains instructional strategies for each domain and cluster. The instructional strategies provide descriptions of effective and promising strategies for
engaging students in observation, exploration and problem solving targeted to
the concepts and skills in the cluster of standards.
Instructional Strategies: Kindergarten
Kindergarteners need to understand the
idea of a ten so they can develop the strategy of adding onto 10 to add within
20 in Grade 1. Students need to construct their own baseten ideas about
quantities and their symbols by connecting to counting by ones. They should use
a variety of manipulatives to model and connect equivalent representations for
the numbers 11 to19.
Instructional Strategies: Grade 1
In this grade, students build on their
counting to 100 by ones and tens beginning with numbers other than 1 as they
learned in Kindergarten. Students can start counting at any number less than
120 and continue to 120. It is important for students to connect different
representations for the same quantity or number.
Instructional Strategies: Grade 2
The understanding that 100 is 10 tens or 100 ones is critical to the understanding of place value. Using proportional
models like baseten blocks and bundles of tens along with numerals on placevalue mats provides connections
between physical and symbolic representations of a number. These models can be used to compare two numbers and
identify the value of their digits.
Instructional Strategies: Grade 3
Prior to implementing rules for rounding students need to have opportunities to investigate place value. A strong
understanding of place value is essential for the developed number sense and the subsequent work that involves
rounding numbers.
Instructional Strategies: Grade 4
Provide multiple opportunities in the classroom setting and use realworld context for students to read and write multidigit
whole numbers.
Students need to have opportunities to compare numbers with the same number of digits, e.g., compare 453, 698 and
215; numbers that have the same number in the leading digit position, e.g., compare 45, 495 and 41,223; and numbers
that have different numbers of digits and different leading digits, e.g., compare 312, 95, 5245 and 10,002.
Instructional Strategies: Grade 5
In Grade 5, the concept of place value is extended to include decimal values to thousandths. The strategies for Grades
3 and 4 should be drawn upon and extended for whole numbers and decimal numbers. For example, students need to
continue to represent, write and state the value of numbers including decimal numbers. For students who are not able
to read, write and represent multidigit numbers, working with decimals will be challenging.
Instructional Strategies: Grade 6
Computation with fractions is best understood when it builds upon the familiar understandings of whole numbers and is
paired with visual representations. Solve a simpler problem with whole numbers, and then use the same steps to solve
a fraction divided by a fraction. Looking at the problem through the lens of “How many groups?” or “How many in each
group?” helps visualize what is being sought.
Instructional Strategies: Grade 7
This cluster in The Number System, builds upon the understandings of rational numbers in Grade 6:
 quantities can be shown using + or – as having opposite directions or values,
 points on a number line show distance and direction,
 opposite signs of numbers indicate locations on opposite sides of 0 on the number line,
 the opposite of an opposite is the number itself,
 the absolute value of a rational number is its distance from 0 on the number line,
 the absolute value is the magnitude for a positive or negative quantity, and
 locating and comparing locations on a coordinate grid by using negative and positive numbers.
Instructional Strategies: Grade 8
The distinction between rational and irrational numbers is an abstract distinction, originally based on ideal assumptions
of perfect construction and measurement. In the real world, however, all measurements and constructions are
approximate. Nonetheless, it is possible to see the distinction between rational and irrational numbers in their decimal
representations.
Instructional Strategies: Number and Quantity
The goal is to show that a fractional exponent can be expressed as a radical or a root. For example, an exponent of
1/3 is equivalent to a cube root; an exponent of ¼ is equivalent to a fourth root.
Instructional Strategies: Algebra
Extending beyond simplifying an expression, this cluster addresses interpretation of the components in an algebraic
expression. A student should recognize that in the expression 2x + 1, “2” is the coefficient, “2” and “x” are factors, and
“1” is a constant, as well as “2x” and “1” being terms of the binomial expression. Development and proper use of
mathematical language is an important building block for future content.
