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Concrete-Representation-Abstract

  • Introduction to Volume – Manipulatives (starting with perimeter and area)

    Introduction to Volume – Manipulatives (starting with perimeter and area)

    Here is a Jamboard to introduce volume and units of volume. (See photo at very bottom for making a copy to edit.) The students start with building an animal pen and shading in the space inside. The hands on approach and connection to prior knowledge of a fenced in area for animals sets the stage…

  • Add vs Subtract Concepts – Kinesthetic Approach

    Add vs Subtract Concepts – Kinesthetic Approach

    In working with students who have fallen significantly behind in math, a common challenge is adding and subtracting. This can manifest in word problems or simple add and subtract problems. When this is the case, the first thing I check is whether the student understands conceptually what addition and subtraction are. Here is a Google…

  • Intro to Solving Equations – Seesaws and Oranges

    Intro to Solving Equations – Seesaws and Oranges

    Here is an introduction to solving equations using a Jamboard (see photo at very bottom for how to make a copy). A seesaw is used to unpack the concept of an equation as two sides that are equivalent. The box is used to unpack the concept of a variable representing an unknown number (or oranges…

  • Combining Like Terms – From Concrete to Symbolic Form

    Combining Like Terms – From Concrete to Symbolic Form

    Here is a Jamboard (see photo at very bottom for how to make a copy to edit) that presents like terms as visual manipulatives and then eases into the symbolic form – the “mathy” stuff. The following shows each slide as is and how it looks after completion. Start with two groups of common items,…

  • Introduction to Pythagorean Theorem

    Introduction to Pythagorean Theorem

    Here is a link to the Jamboard (make a copy to edit – see photo at the very bottom). The directions are on each slide. The photos below show what the results should look like. To make a copy, click 3 dots and choose copy.

  • Introduction to Absolute Value – Distance from Home

    Introduction to Absolute Value – Distance from Home

    Here is a Jamboard to introduce the concept of absolute value (make a copy and you can edit – see photo at bottom of this post). Start with prior knowledge of how many houses a child is from home. Emphasize that the number of houses is positive. Change the setting from a row of houses…

  • Multi-step Word Problems – Create Groups of Items

    Multi-step Word Problems – Create Groups of Items

    Here is a Google Slides file as a follow up to the Multiplication Word Problems Matching and Creating Groups post. Each slide has a multi-step word problem (multiplication and either addition or subtraction) that continues the use of the grouping approach. The boxes (for groups) and dots (for items) and dynamic and can be copied…

  • Matching Activity for Multiplication Word Problems (and Creating)

    Matching Activity for Multiplication Word Problems (and Creating)

    Here is a matching activity on a Google Slides file for various multiplication word problems and matching groups of items. The students use gallery view of the slides and sort them to match. Then they can change the background color with a different color for each word problem and groups. This allows them a visual…

  • Intro to Ratio Tables

    Intro to Ratio Tables

    If you find this helpful, maybe consider making a small donation to help build an accessible playscape for children with disabilities. To introduce ratio tables, I draw upon a relevant prior knowledge for a child. Food, especially pizza is a go to context for me. Use a CRA approach by using manipulatives (concrete), pictures (representational),…

  • Group Model for Proportional Relationships and Slope Application

    Group Model for Proportional Relationships and Slope Application

    If you find this helpful, maybe consider making a small donation to help build an accessible playscape for children with disabilities. In my experience, many students struggle with translating word problems modeled by a proportional relationship or a linear function into a algebraic expression or equation. (Image below.) Here is a link to a Jamboard…