Number Bonds are a crucial component of early Singapore Math programs.  Number Bonds consist of a minimum of 3 circles connected with lines, and they provide a pictorial representation of part-part-whole relationships.

A child who knows this bond should be able to immediately fill in any one of these three numbers if it was missing, given the other two.  Work with these bonds is a fundamental part of building mental math fluency.

Here are 3 resources for teachers who want to introduce early elementary students to number bonds:

1)  Number Bond Sprints for Grade 1 (A good introduction, from EngageNY)

2)  Interactive Number Bonds for PK-K

3)  Bonds to 1, 10, 20, and 100 from WMNET

Tape Diagrams are models that students draw to help them visualize the relationships between the quantities.  The models open the door to efficient problem solving, and help students see the coherence in the mathematics across the years.  This Powerpoint from EngageNY, which they call their “Tape Diagrams Coherence Presentation“, is a nice introduction to how tape diagrams can be used effectively with a “Read, Draw, Write” approach to problem solving.  They’re particularly useful for teaching Ratios.

EngageNY’s Modular Curriculum contains “Singapore Sprints“, fluency activities which are designed to improve automaticity. Sprints were invented by Dr. Yoram Sagher, professor of Mathematics at Florida Atlantic University.  These math races are focused on patterns, and they are delivered in a fun, exciting, and competitive environment.  The Sprints within EngageNY’s Curriculum were designed by Bill Davidson, and here are some tips for quickly locating that specific content from the mass of curriculum materials.

• Start by going to the EngageNY Curriculum Module Site, and open a Module for your grade level.
• Hold the CTRL button down on your keyboard, and then press F.
• In the search field that appears, type “Sprint”.

This will allow you to find every occurrence of the word “Sprint” within the PDF.  You can then print only the Sprints you’d like to use with your class.

What other components of Singapore Math have you found resources for that you’d like to share?