TeachTown’s enCORE solution is the only standards-based, core-curriculum based on Applied Behavior Analysis (ABA) that provides students with moderate and severe disabilities, including students with autism and other intellectual and developmental disabilities, access to the general education curriculum. Read on to learn more about each segment within enCORE’s Math Lessons.

enCORE is a comprehensive approach to delivering grade-aligned academic instruction for students with moderate to severe disabilities. The math domain of the K-12 adapted core curriculum was designed with the evidence-based instructional practices found throughout enCORE, including the principles of Applied Behavior Analysis and systematic, explicit instruction.

Each math lesson is structured to flow through the gradual release of responsibility, guiding students towards greater independence as they show they are ready. Lesson plans begin with anchored instruction to help students connect the new learning objective to their existing background knowledge and to make connections to their everyday lives. Then, teachers move through this sequence:

- Direct instruction and modeling
- Shared instruction and guided practice
- Independent student practice with ongoing teacher monitoring

This progression is noted within the print lesson plans as ‘Model, Lead, Test’ and will likely be familiar to educators as the I Do, We Do, You Do model.

Introducing students to new skills in small, bite-sized pieces supports complex learners by ensuring students receive multiple exposures to the new skill, prompting and feedback to avoid practicing incorrectly, and plenty of practice to reinforce new learning.

- Click here to see a sample
**enCORE Elementary Math Lesson Plan** - Click here to see a sample
**enCORE Middle Math Lesson Plan** - Click here to see a sample
**enCORE High Math Lesson Plan**

The math domain also includes evidence-based instructional practices that are specific to math, including concrete representations, the use of technology, and connecting math to real-world events.

Concrete representations, or math manipulatives like ten-frames and counting toys, are available throughout the enCORE curriculum for elementary, middle, and high school students. Lessons incorporate many everyday items that are found in the classroom. For example, in one elementary lesson, students learn to distinguish between thin and thick by comparing books of different sizes.

The specific math manipulatives included in each grade band are shown below in the manipulative kit item lists:

- enCORE Elementary Math Manipulatives
- enCORE Middle Math Manipulatives
- enCORE High Math Manipulatives

Concrete representations help make math concepts and operations less abstract, more concrete, and relevant to students’ lives. For example, students who practice concepts about money with coins and dollar bills are much more likely to generalize those concepts to their everyday lives.

The use of technology through the teacher-facilitated and student-led lessons in the learning platform further supports the use of concrete representations in the form of virtual manipulatives, like visuals on the screen that represent a quantity or an online clock.

Technology is also used to help anchor instruction by making math operations more applicable to day-to-day activities and to literature stories.

Literature reviews identify the use of math problems that represent real-life scenarios as an evidence-based practice for teaching math. This is one way to anchor instruction. Math instruction in every unit of enCORE Elementary is anchored in problems that are meaningful by using the literature embedded in the curriculum. For example, word problems designed to teach problem-solving skills and basic math operations focus on the characters and scenarios for the book that anchors that particular unit.

The lesson plan snapshot below shows a sample word problem related to the characters and scenarios from a unit in enCORE Elementary. The book for this unit is The Swiss Family Robinson. Students practice modeling single-digit addition and subtraction math problems through the context of the characters in the Robinson family (e.g., collecting sticks, building a fire, etc.).

While enCORE Elementary makes connections from the new math concept to the unit’s literature throughout the lesson plans, enCORE Middle and enCORE High primarily make these connections during the anchor instruction portion of the lesson plans (e.g., the beginning part of the lesson). Activating background knowledge helps older students make sense of new math concepts by drawing upon existing references but also honors the developmental advancement of both the literature and math as the lessons progress.

EnCORE Math incorporates real-world math applications alongside standards-based activities and practices for all grade bands. Skills like budgeting, time management, and other skills that students with low-incidence disabilities may not learn incidentally are explicitly taught and reinforced through warm-up worksheets. These skills are spiraled where appropriate throughout the lesson plans so that students have opportunities to apply foundational concepts to their everyday lives.

Students learn how to:

- Read a bus schedule and plan accordingly
- Account for traffic when deciding what time to leave the house to arrive on time
- Save enough money to make a desired purchase

And much more!

These everyday math skills are reinforced to ensure these **foundational skills are acquired, retained, and generalized** to support their transition to adulthood & the appropriate level of independence after high school.

Let’s take a look now at the specific math content in each of the grade bands.

In enCORE Elementary, the Math domain includes 8 areas of focus.

The **Counting and Cardinality Segment** addresses number identification, number sense, rote counting, counting quantities with one-to-one correspondence, and sequencing numbers and quantities. These early numeracy skills provide a strong foundation in what numbers mean and how they relate to the objects in our world, allowing students with moderate to severe disabilities a firm footing for jumping into the content included in other Math segments.

In the **Operations and Algebraic Thinking Segment**, students are guided through pre-problem-solving and problem-solving activities. Math is brought to life using relatable story problems, and students are taught to identify critical information from a problem and the steps necessary to solve the problem using evidence-based support.

The **Measurement and Data Segment** addresses measurable attributes of physical objects, sorting and comparing those objects, and graphing and analyzing data. Students and teachers work side by side to complete hands-on activities based both in the curriculum’s literature and in real-world scenarios.

The **Math All Around Us Segment** addresses two key areas: (1) extending skills taught in other segments as they relate to the world around us, and (2) how we can draw skills from multiple math domains and use them in tandem to solve problems in the education classroom and beyond. [Add another sentence like …] This segment gives students additional practice with newly acquired skills and the valuable opportunity to connect seemingly abstract concepts to their everyday lives.

Each **Number and Operations in Base 10** (or Fractions, for Units 19-36 in the 3-5 band) **Segment** provides teachers and students with hands-on materials and graphic organizers needed to develop conceptual knowledge and clear comprehension of how numbers, quantities, and individual objects can be put together, organized, and taken apart. These lessons encourage students to practice numeracy skills in the context of Base 10 units, tens, and hundreds and in the context of the parts and wholes represented by fractions. Students will bring these skills together to solve equations and word problems using Base 10 Units and fractions.

The **Time Segment** is designed to address the functional math skills we use daily. From identifying time on various devices to identifying money and making purchases in the community, teachers are provided with scripted step-by-step instructions on how to teach these critical math concepts.

The **Money Segment** is designed to familiarize students with coins and dollar bills and support them in developing a sense of their value, both in relation to other currencies (e.g., “A $20 bill is worth more than a quarter.”) and in relation to their value in everyday situations (e.g., “I can buy more with a $20 bill than a quarter, but someone should not ask me to pay $20 for a pack of gum.”). These lesson segments focus on identifying coins and bills, counting the value of money, and employing practical strategies to use money effectively in the real-world environment.

The Geometry Segment teaches students to identify two-dimensional and three-dimensional shapes. Additionally, students are taught to identify the attributes of shapes, compare shapes by their attributes, and identify and extend patterns.

In enCORE Middle, the Math domain includes 6 areas of focus:

**The Number System****Expressions & Equations****Statistics & Probability****Geometry, Ratios & Proportions**(6th and 7th grade)**Functions**(8th grade)

Each of the middle school grades (6-8) covers 9 units of instruction per year. **The Number System** covers instruction on positive and negative numbers and rational and irrational numbers. **Expressions and Equations** introduce and build understanding related to written and graphed linear equations, expressions, and inequalities. **Statistics and Probability** contains instruction in collecting, organizing, and displaying data, as well as reading data and making predictions. **Geometry** covers lines, angles, geometric relationships, and polygons (including triangles and quadrilaterals). **Ratios and Proportions** introduce concepts in comparing quantities and graphing proportional relationships. The **Functions** units contain instructions on determining linear functions and their components (both algebraically and graphically).

Within each unit, there are 2 lesson plans, each containing 4 segments that focus on clear, specific learning objectives derived from state and national Math standards.

- The
**Math Momentum I**segment introduces new topics and reviews prerequisite skills, setting students up to learn more complex, multi-step concepts in later segments within the lesson. - In the
**Math Foundations I**segment, students are introduced to problem-solving and multi-step tasks. - The
**Math Foundations II**segment expands on the content covered in Math Foundations I. - The fourth segment,
**Math Exploration,**requires students to solve more complex problems using the skills they have developed over subsequent segments. The instruction in this segment serves as the culmination of a series of scaffolded skills.

At the end of each lesson plan are **Generalization and Extension Activities**. The Generalization and Extension Activities provide students with extended practice and helps them generalize learned skills and can be completed at times that work with a classroom schedule.

In enCORE High School, the Math domain includes 4 standard mathematics courses:

**Algebra 1, Geometry, Algebra II, and Probability, Statistics, and Logic.** The order the courses are presented, corresponding to grade band 9-12, can be shifted when required by district or state guidelines. Each course contains nine units of instruction, equating to one year of instruction. The Algebra I and II courses incorporate instruction that encompasses Algebraic Reasoning and Functions (Equations and Inequalities). The Geometry course instruction covers standards in Geometry and Measurement. And during the Probability, Statistics, and Logic course units, students will receive instruction covering Data Analysis, Statistics, and Probability, as well as Numbers, Operations, and Logic. Each course consists of eight units of instruction and concludes with a ninth unit of **Financial Literacy**.

Within each unit are 2 lesson plans, each containing 5 segments that focus on clear, specific learning objectives derived from state and national Math standards.

- The
**Math Momentum I**and**II**segments introduce new topics and review prerequisite skills, setting students up to learn more complex, multi-step concepts in later segments within the lesson. - In the
**Math Foundations I**segment, students are introduced to problem-solving and multi-step tasks. - The
**Math Foundations II**segment expands on the content covered in Math Foundations I. - The fifth segment,
**Math Exploration,**requires students to solve more complex problems using the skills they have developed over subsequent segments. The instruction in this segment serves as the culmination of a series of scaffolded skills.

At the end of each lesson plan are five **Math for Life: Generalization and Extension Activities**. The Generalization and Extension Activities focus on skill development in the areas of Community, Vocational, Home, Personal Life, and Leisure.