Mathematical foundations, such as number sense, operations, and algebraic thinking, are critical skills for elementary students to master. Students who struggle with foundational math concepts often benefit from targeted tier 2 interventions to help fill learning gaps and allow them to keep up with grade-level material. Here are some examples of effective tier 2 math interventions focused on foundations:
Number Sense Interventions
- Small group instruction targeting counting, cardinality, and quantity comparison. Hands-on activities with manipulatives can build number sense. For example, having students count out a certain number of objects, compare sets to identify greater than/less than, or sequence numbers.
- Math games and apps that provide practice with rote counting, number recognition, and comparing quantities. Students work at their skill level and get repeated practice.
- Use of visual representations like ten frames, number lines, and hundreds charts to reinforce counting and quantity. Students can use these tools to subitize, count on, or visualize numbers.
Operations Interventions
- Targeted instruction on understanding and modeling addition, subtraction, multiplication, and division. Use manipulatives and visual models to build conceptual understanding before introducing algorithms.
- Practice with math facts and families to build fluency. Games, flashcards, and timed activities allow repetition.
- Word problem instruction to apply operation sense. Use visual models and diagrams to represent problems.
Algebraic Thinking Interventions
- Activities focused on identifying, extending, and creating patterns. Have students analyze pattern core/rules, continue patterns, and make predictions.
- Practice with equality and inequality using balance scales or pictures. Have students model equalities with manipulatives and explain their reasoning.
- Give examples finding missing numbers in equations, such as: __ + 5 = 7. Use this to teach the concept of variables.
Progress Monitoring
- Short 1-3 minute math fluency probes, given weekly or biweekly, to assess counting, facts, and computation.
- Curriculum-based measures that align with current math standards and content. These can identify skill deficits.
- Observation and work sample review to check for understanding of foundational concepts.
Universal screening tools like i-Ready or MAP Growth can identify students in need of tier 2 interventions. Progress monitoring allows teachers to track growth and adjust instruction accordingly. Targeted small group instruction and practice builds the foundations to support higher level math learning.
Here are some hands-on lesson plans for foundational math using a Rekenrek 100-Bead Wood, Individual Student Counting Frame:
**Lesson 1: PreSchool- Kindergarten Introduction to the Rekenrek Counting Frame**
* Objectives:
* Students will be able to identify the different parts of the Rekenrek counting frame.
* Students will be able to count objects using the Rekenrek counting frame.
* Materials:
* Rekenrek counting frames for each student
* Small objects, such as beads, buttons, or counters
* Procedure:
1. Begin by reviewing the different parts of the Rekenrek counting frame with students. Point out the rods, the beads, and the frame.
2. Next, demonstrate how to count objects using the Rekenrek counting frame. Show students how to slide the beads along the rods to represent different numbers.
3. Give each student a Rekenrek counting frame and some small objects. Have students practice counting the objects using the Rekenrek counting frame.
4. As students are counting, circulate around the room and provide assistance as needed.
**Lesson 2: Comparing Numbers Using the Rekenrek Counting Frame**
* Objectives:
* Students will be able to compare two numbers using the Rekenrek counting frame.
* Students will be able to identify which number is greater or less than another number.
* Materials:
* Rekenrek counting frames for each student
* Small objects, such as beads, buttons, or counters
* Procedure:
1. Begin by reviewing how to count objects using the Rekenrek counting frame with students.
2. Next, demonstrate how to compare two numbers using the Rekenrek counting frame. Show students how to slide the beads along the rods to represent different numbers.
3. Give each student a Rekenrek counting frame and some small objects. Have students practice comparing two numbers using the Rekenrek counting frame.
4. As students are comparing numbers, circulate around the room and provide assistance as needed.
**Lesson 3: Adding and Subtracting Numbers Using the Rekenrek Counting Frame**
* Objectives:
* Students will be able to add and subtract numbers using the Rekenrek counting frame.
* Students will be able to solve simple addition and subtraction problems using the Rekenrek counting frame.
* Materials:
* Rekenrek counting frames for each student
* Small objects, such as beads, buttons, or counters
* Procedure:
1. Begin by reviewing how to count objects using the Rekenrek counting frame with students.
2. Next, demonstrate how to add and subtract numbers using the Rekenrek counting frame. Show students how to slide the beads along the rods to represent different numbers.
3. Give each student a Rekenrek counting frame and some small objects. Have students practice adding and subtracting numbers using the Rekenrek counting frame.
4. As students are adding and subtracting numbers, circulate around the room and provide assistance as needed.
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