Understanding the Math Instruction Plan Sequence

Description

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Numbers and Operations. This instructional focus is generally consistent with On Track performance at the PreK and Early Kindergarten levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to (a) Read, recognize, and write number symbols or names to 20. Instruction also promotes Operations skills to (a) Know number names and number sequence (forward to 20, backward from 10); (b) Count forward from a given number without having to start at 1; (c) Count to tell the number of objects; can compare two numbers and tell which is bigger/smaller; and (d) Understand that adding is “putting together” and subtracting is “taking from.”

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Numbers and Operations. This instructional focus is generally consistent with On Track performance at the Early to Middle Kindergarten levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to (a) Read, recognize, and write number symbols or names greater than 20; (b) Understand that while counting, the next number has a quantity of one more; the previous number one less, and (c) Compose and decompose numbers 11 through 19 into tens and ones to gain a foundation for place value. Instruction also promotes Operations skills to (a) Know number names and number sequence (first to 31, then to 100, by ones and tens, and from a given number); (b) Count to answer “how many” questions; (c) Compare numbers of objects, including quantities represented by two written numerals; (d) Compose and decompose numbers less than or equal to 10 into pairs in multiple ways; record with a drawing or equation; (e) Apply number concepts and whole number operations to solve concrete, real-world problems.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on General Math skills in multiple math domains. This instructional focus for this plan is generally consistent with On Track performance at the Mid-fall Kindergarten to Late Kindergarten level, and sometimes Early Kindergarten. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Geometry and Measurement skills to (a) Work with shapes by analyzing, comparing, creating, and composing; and (b) Classify objects into categories; count the number of objects in each category. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Numbers and Operations. This instructional focus is generally consistent with On Track performance at the Early to Middle first-grade level. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to understand base-10 (place value; that 2-digit numbers represent 10s and 1s; decade numbers). Instruction also promotes Operations skills to (a) Extend the counting sequence to 120 and above, including reading and writing number symbols and names; (b) Add and subtract within 20; and (c) Work with addition and subtraction equations and problems using properties of operations and relating addition to subtraction. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the Middle to Late first-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Operations skills to Whole Numbers: (a) Use place value and properties of operations to add and subtract; (b) Apply number and operations concepts and skills to represent and solve addition and subtraction equations and problems. The initial focus should promote accuracy and then progress to automaticity and fluency. Instruction promotes Automaticity and Fluency to add and subtract within 20 and higher.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on General Math skills in multiple math domains. The instructional focus for this plan is generally consistent with On Track performance at the Middle to Late first-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Reason with shapes and their attributes (build and draw shapes, partition shapes into 2 and 4 equal shapes, and describe using the language of “halves,” “wholes,” “fourths”); (b) Measure lengths indirectly (comparing to another length object) or by repeated length units; represent length as a whole number; and (c) Tell and write time (hours and half-hours using digital and analog clocks). Instruction also promotes skills in Data, Statistics, and Probability to represent data by categorizing and comparing the number of items in different categories. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Numbers and Operations. This instructional focus is generally consistent with On Track performance at the Early to Middle second-grade level. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to (a) Understand place value applied to larger numbers up to 1,000. Instruction also promotes Operations skills to (a) Count to 1,000 (also skip count by fives, tens, and hundreds; read and write number symbols and names, and use expanded form); (b) Represent and solve one- and two-step addition and subtraction word problems within 100 (some involving time, money, length); (c) Add and subtract within 1,000; and (d) Build a foundation for understanding multiplication. Instruction also promotes Rational Numbers skills to develop early fraction concepts: understand and describe equal portions of whole numbers using the language of fractions. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the Middle to Late second-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Operation skills to (a) Develop automaticity with early fraction concepts, including using the language of fractions; (b) Know all sums of one-digit numbers from memory, and quickly use them to compute; and (c) Fluently add and subtract within 100. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on General Math skills in multiple math domains. The instructional focus for this plan is generally consistent with On Track performance at the Middle to Late second-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Reason with shapes and their attributes; (b) Measure and estimate lengths in standard units (inches, feet, centimeters, meters); (c) Represent whole numbers within 100 as lengths on a number line; (d) Work with time and money; and (e) Solve problems using measurement involving time, money, and length. Instruction also promotes skills in Data, Statistics, and Probability to collect, represent (pictographs, bar graphs), and interpret data. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Numbers and Operations. This instructional focus is generally consistent with On Track performance at the Early to Middle third-grade level. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to (a) Understand properties of multiplication and the relationship between multiplication and division; (b) Understand concepts of the area; relate to addition and multiplication; and (c) Understand the concept of the perimeter; distinguish from area measures. Instruction also promotes Operations in Whole Number skills to (a) Use place value to understand and describe properties of operations to solve multi-digit problems within 1,000; (b) Solve word problems (including two-step) using all four operations, and multiplication and division within 100; (c) Use a letter for an unknown quantity, and identify and explain arithmetic patterns; and (d) Memorize all products of two single-digit numbers. This plan also promotes skills with Rational Numbers to understand fractions as numbers. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the Middle to Late third-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Operation skills to automatically and fluently multiply and divide within 100 by using mental strategies. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on General Math skills in multiple math domains. The instructional focus for this plan is generally consistent with On Track performance at the Middle to Late third-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Reason with shapes and their attributes; (b) Solve problems involving perimeters and areas; and (c) Solve problems using measurement and estimation of liquid volumes, masses, and time intervals. Instruction also promotes skills in Data, Statistics, and Probability to collect, represent (pictographs, bar graphs), and interpret data. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the fourth and fifth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to generalize understanding of place value to solve problems with multi-digit numbers as well as use Rational Number skills (fractions and decimals). In addition, this plan promotes Operations skills for Whole and Rational Numbers as well as introductory Algebra skills related to expressions, patterns, and relationships. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the Middle to Late fourth and fifth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math in Geometry and Measurement skills to (a) Solve measurement problems that involve and require conversion (e.g., from larger to smaller units, decimals, fractions); (b) Understand concepts of volume and relate to multiplication and division; (c) Identify and draw lines and angles and classify two-dimensional figures according to their line and angle attributes; and (d) Graph coordinate pairs in the context of real and mathematical problems. This plan also promotes the use of Data, Statistics, and Probability skills to represent and interpret data involving fractions and line plots. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the fourth and fifth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes Number skills to generalize understanding of place value to solve problems with multi-digit numbers as well as use Rational Number skills (fractions and decimals). In addition, this plan promotes Operations skills for Whole and Rational Numbers as well as introductory Algebra skills related to expressions, patterns, and relationships. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the Middle to Late fourth and fifth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math in Geometry and Measurement skills to (a) Solve measurement problems that involve and require conversion (e.g., from larger to smaller units, decimals, fractions); (b) Understand concepts of volume and relate to multiplication and division; (c) Identify and draw lines and angles and classify two-dimensional figures according to their line and angle attributes; and (d) Graph coordinate pairs in the context of real and mathematical problems. This plan also promotes the use of Data, Statistics, and Probability skills to represent and interpret data involving fractions and line plots. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction extends Number skills to the system of all rational numbers, including negative numbers. Instruction also promotes Operations in Whole and Rational Number skills related to proportional relationships and problem-solving, including Algebra skills for solving expressions and equations, modeling an association in bivariate data with a linear expression, and solving linear equations and systems of linear equations. This plan introduces the concept of a function and the use of functions to describe quantitative relationships. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Solve real-world and mathematical problems involving angle measure, area, surface area, and volume (including that of cubes, cylinders, cones, and spheres); (b) Understand congruence and similarity using physical models, transparencies, or geometric software; and (c) Understand and apply the Pythagorean Theorem. This plan also promotes the use of Data, Statistics, and Probability skills to (a) Develop an understanding of statistical thinking, including drawing inferences about populations based on samples; and (b) Investigate chance processes; develop, use, and evaluate probability models. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction extends Number skills to the system of all rational numbers, including negative numbers. Instruction also promotes Operations in Whole and Rational Number skills related to proportional relationships and problem-solving, including Algebra skills for solving expressions and equations, modeling an association in bivariate data with a linear expression, and solving linear equations and systems of linear equations. This plan introduces the concept of a function and the use of functions to describe quantitative relationships. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Solve real-world and mathematical problems involving angle measure, area, surface area, and volume (including that of cubes, cylinders, cones, and spheres); (b) Understand congruence and similarity using physical models, transparencies, or geometric software; and (c) Understand and apply the Pythagorean Theorem. This plan also promotes the use of Data, Statistics, and Probability skills to (a) Develop an understanding of statistical thinking, including drawing inferences about populations based on samples; and (b) Investigate chance processes; develop, use, and evaluate probability models. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction extends Number skills to the system of all rational numbers, including negative numbers. Instruction also promotes Operations in Whole and Rational Number skills related to proportional relationships and problem-solving, including Algebra skills for solving expressions and equations, modeling an association in bivariate data with a linear expression, and solving linear equations and systems of linear equations. This plan introduces the concept of a function and the use of functions to describe quantitative relationships. The initial focus should promote accuracy and then progress to automaticity and fluency.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Solve real-world and mathematical problems involving angle measure, area, surface area, and volume (including that of cubes, cylinders, cones, and spheres); (b) Understand congruence and similarity using physical models, transparencies, or geometric software; and (c) Understand and apply the Pythagorean Theorem. This plan also promotes the use of Data, Statistics, and Probability skills to (a) Develop an understanding of statistical thinking, including drawing inferences about populations based on samples; and (b) Investigate chance processes; develop, use, and evaluate probability models. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes fluency with Number skills that include complex numbers, vectors, and matrix quantities as well as the properties of irrational numbers. This plan also promotes Operations in Whole and Rational Number skills for operations involving complex numbers, vectors and matrices, and polynomials, and rational exponents. The plan extends Algebra skills for solving expressions, equations, and inequalities and using functions to model relationships, compare models, and solve problems.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the ninth to twelfth-grade levels. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Extend and apply knowledge of geometry and measurement to address real-world problems; and (b) Understand and apply properties of transformations, similarity, right triangles, trigonometry, and circles. This plan also promotes the use of skills in Data, Statistics, and Probability to (a) Extend and apply knowledge of statistics to address real-world problems; (b) Make inferences and justify conclusions to interpret categorical and quantitative data; and (c) Understand and apply rules of probability and statistical modeling to make decisions. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes fluency with Number skills that include complex numbers, vectors, and matrix quantities as well as the properties of irrational numbers. This plan also promotes Operations in Whole and Rational Number skills for operations involving complex numbers, vectors and matrices, polynomials, and rational exponents. The plan extends Algebra skills for solving expressions, equations, and inequalities and using functions to model relationships, compare models, and solve problems.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the ninth to twelfth-grade levels. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Extend and apply knowledge of geometry and measurement to address real-world problems; and (b) Understand and apply properties of transformations, similarity, right triangles, trigonometry, and circles. This plan also promotes the use of skills in Data, Statistics, and Probability to (a) Extend and apply knowledge of statistics to address real-world problems; (b) Make inferences and justify conclusions to interpret categorical and quantitative data; and (c) Understand and apply rules of probability and statistical modeling to make decisions. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes fluency with Number skills that include complex numbers, vectors, and matrix quantities as well as the properties of irrational numbers. This plan also promotes Operations in Whole and Rational Number skills for operations involving complex numbers, vectors and matrices, polynomials, and rational exponents. The plan extends Algebra skills for solving expressions, equations, and inequalities and using functions to model relationships, compare models, and solve problems.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the ninth to twelfth-grade levels. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Extend and apply knowledge of geometry and measurement to address real-world problems; and (b) Understand and apply properties of transformations, similarity, right triangles, trigonometry, and circles. This plan also promotes the use of skills in Data, Statistics, and Probability to (a) Extend and apply knowledge of statistics to address real-world problems; (b) Make inferences and justify conclusions to interpret categorical and quantitative data; and (c) Understand and apply rules of probability and statistical modeling to make decisions. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on both Numbers and Operations. This instructional focus is generally consistent with On Track performance at the sixth to eighth-grade levels. Students in later grades who are at some or high risk for math difficulties may also benefit from this plan. The focus of instruction promotes fluency with Number skills that include complex numbers, vectors, and matrix quantities as well as the properties of irrational numbers. This plan also promotes Operations in Whole and Rational Number skills for operations involving complex numbers, vectors and matrices, polynomials, and rational exponents. The plan extends Algebra skills for solving expressions, equations, and inequalities and using functions to model relationships, compare models, and solve problems.

Based on screening data, this plan is recommended when there is a need for supplemental instruction with a focus on Operations. This instructional focus is generally consistent with On Track performance at the ninth to twelfth-grade levels. The focus of instruction promotes General Math skills in Geometry and Measurement to (a) Extend and apply knowledge of geometry and measurement to address real-world problems; and (b) Understand and apply properties of transformations, similarity, right triangles, trigonometry, and circles. This plan also promotes the use of skills in Data, Statistics, and Probability to (a) Extend and apply knowledge of statistics to address real-world problems; (b) Make inferences and justify conclusions to interpret categorical and quantitative data; and (c) Understand and apply rules of probability and statistical modeling to make decisions. Refer to your school’s grade-level curriculum and standards for additional guidance and instructional targets.

Based on screening data, this plan is recommended when results indicate that regular core instruction meets the needs of this student. Continue to provide high-quality whole-group instruction. This should include instruction and practice in Numbers, Operations, and General Math domains so that this student’s math skills are accurate, automatic, and fluent, and the student can generalize their skills to a variety of math areas.