Five IEP Math Lesson Plans for Addition and Subtraction

Introduction: IEP Focus Learner and Learning Goal

An Individualized Education Program (IEP) is devised for a student who needs special attention in a subject area where she demonstrates particular weakness. Her performance is notably below the class average, yet she participates in regular classroom sessions. Learning alongside other students can help her gain a deeper understanding of the concepts being studied. This paper formulates five detailed math lesson plans for an IEP focus learner targeting addition and subtraction equations. The infusion of tactile and visual supports is encouraged throughout, as the selected focus learner requires foundational scaffolding to solve equations successfully.

Lesson Plan 1: Addition by Counting Onward

Lesson Objective: The focus learner will add one- and two-digit numbers by counting onward when provided a visual prompt, with 80% accuracy.

Initially, the focus learner will receive explicit instruction on adding two-digit numbers by counting onward, working on her fingers or mentally rather than relying on her whiteboard or hundreds chart. Each step of the method will be carefully explained so that it is fully internalized. Although her current mental understanding is at the Kindergarten level and one-digit addition is most appropriate at this stage, the teacher may introduce mixed-digit sums — for example, adding 9 to 23. To achieve the 80% accuracy target, the focus learner will be taught how to align the ones and tens of two-digit numbers. Once she can mentally compute the ones and tens columns separately, she will be better prepared for more complex addition sums.

Complexity will be increased incrementally by raising the number of digits, in alignment with the Common Core standard of fluently adding within 1,000. Using the algorithm method alongside the place value knowledge the focus learner already possesses will reinforce her understanding of three-digit numbers — specifically the placement of units, tens, and hundreds. The strategy-based method will also be introduced, whereby a three-digit number is decomposed into its respective place values for addition according to correct positioning. Because the focus learner is already familiar with place values, she will practice this skill repeatedly with several equations during class.

Visuals will support the focus learner's development of counting onward for addition. For example, real-world questions involving priced items — such as a table costing $110 and a chair costing $50 — will give her the opportunity to practice both the strategy-based and algorithm methods while developing fluency. Incorporating money into these visual exercises will additionally strengthen her understanding of currency, an identified area of weakness.

Simple worksheets presenting a combination of equations in both written and algorithm forms will also be used. The purpose is to sharpen her ability to transfer equations into algorithm form for computation and to practice counting onward digit by digit. Combinations will include adding a one-digit number to a three-digit number, a two-digit number to a three-digit number, and a three-digit number to a three-digit number — encouraging full grasp of regrouping as well.

Online educational games offer an engaging way for the focus learner to actively practice counting onward for addition. The structured game interface guides the user through steps in a systematic way, helping the focus learner understand the sequence of addition without error. The built-in feedback function — informing the user whether an answer is correct — will also allow the focus learner to gauge whether her score approaches the 80% accuracy target (Education.com, n.d.).

Guided prompts will be used during the introductory phase of the one-year plan — approximately one week — and then withdrawn so the focus learner can practice independently. Occasionally, once or twice a week, guided prompts may be reintroduced so the learner knows support is always available.

Tactile supports are an important component, especially for beginning addition with one-digit numbers and regrouping. For example, colored pencils can help the focus learner count accurately: if she needs to add 8 to 367, she can count forward — 368, 369, 370, and so on — using pencils as a physical counting aid.

Immediate reinforcement will consolidate the learned methods, strategies, and concepts. At the end of each class, the instructor will ask the focus learner short questions about the lesson's content — a form of informal assessment. The targeted communication skills are responding and describing, in support of an expressive communication goal.

Lesson Plan 2: Subtraction by Counting Backward

Lesson Objective: The focus learner will subtract one- or two-digit numbers by counting backward when provided a visual prompt, with 80% accuracy.

The planned supports for this lesson mirror those in Lesson Plan 1, as the same instructional approach is used to help the focus learner understand counting backward in subtraction. Explicit instruction will begin with two-digit subtraction, then progress to three-digit numbers within 1,000. The focus learner will be encouraged to count backward on her fingers without relying on her whiteboard. The instructor may start at the most basic level — for example, subtracting 7 from 35 — and use mixed-digit computations to reinforce number placement in the algorithm method. Because the focus learner is already familiar with place values, she will be able to align the units column of a one-digit number beneath the tens and units columns of a two-digit number and calculate the difference at the desired 80% accuracy.

Place value will again serve as an additional support for both the strategy-based and algorithm methods. When three-digit computation is introduced, the focus learner will decompose the respective place values and subtract the digits of the second number by counting backward without difficulty.

Visual supports will also be used. For example, word problems involving real-world contexts — such as comparing the number of seats in two sections of a stadium (e.g., 458 versus 342) — will give the focus learner meaningful practice with the strategy-based and algorithm methods using pictures on worksheets. These exercises capitalize on her visual strength, helping her translate visual information into subtraction equations.

Worksheets with a combination of equations and algorithm-formatted questions will be used for practice. Questions will mix one-digit, two-digit, and three-digit numbers — for example, 321 minus 25 or 568 minus 76 — to train place value and backward-counting skills toward 80% accuracy.

Online games that use subtraction problems across all digit sizes will provide additional interactive practice. The systematic game interface automatically guides the focus learner through each step, and built-in scoring lets her determine whether her performance is approaching the 80% accuracy benchmark.

Guided prompts will again be minimized to promote independent work, but will be available during the inaugural weeks and revisited once or twice weekly throughout the plan. Tactile supports — such as thumbtacks — will also be used. If the focus learner needs to subtract 6 from 475, for example, she can count backward using thumbtacks: 475, 474, 473, and so on.

Immediate reinforcement will consolidate the subtraction methods and may take the form of a short quiz at the end of class. Communication goals of responding and describing are again targeted so that expressive communication is encouraged.