Coordinating Units
The videos on this page describe the Coordinating Units (CU) instructional sequence. This sequence is designed to foster children’s development of the initial conceptual foundations for the base-10 place value system. It provides the basis for reasoning that involves coordinating units of ten with units of one. Development of coordinating units reasoning is necessary for children to be able to add and/or subtract numbers greater than twenty. It is necessary for children to develop coordinating units reasoning before they are introduced to the U. S. standard algorithm (or any other algorithm) for adding and subtracting whole numbers greater than twenty.
Teachers that have used the Structuring Numbers instructional sequence will notice similarities with how the Coordinating Units sequence progresses. In both sequences students work with a single quantity in Part I of the sequence and then in Part II shift to working with tasks that involve changing the initial quantity by adding more or taking some away. Likewise, within each of Parts I and II, students shift from using physical materials, the arithmetic rack in the case of the Structuring Numbers sequence and Unifix cubes in the case of the Coordinating Units sequence, to reasoning from visual imagery.
Videos
Video Group 1: Sequence Overview and Coordinating Units Part I – Becoming Efficient With Reasoning About Coordinating Units With A Single Quantity
This video group provides an overview of the entire instructional sequence and a detailed description of Part I of the sequence, “Becoming Efficient With Reasoning About Coordinating Units With A Single Quantity.” There are three segments that comprise this set of videos.
Video Segment 1.1
This first segment begins with an overview of Part 1 of the Coordinating Units instructional sequence. This overview is followed by an introduction to the Candy Shop scenario and a detailed description of the first two activities of Part I of the sequence, Packing Candies and Circling Candies. The purpose of a scenario is to create a realistic situation within which students can reason. The story creates the background for the physical activity the children engage in, which eventually evolves into reasoning about quantities.
Video Segment 1.2
This segment of Part I introduces the Candy Flash activity. The purpose of the flashing activity is to encourage children to advance in their reasoning from mentally moving pieces in their mind and counting to reasoning quantitatively. For example, instead of imagining 4 specific pieces from a group of 5 pieces to place with 6 others in the visual to make ten, they reason that 4 and 6 make ten no matter the location in the visual.
Video Segment 1.3
This last segment of Part I introduces the Transformation activity. The purpose of the transformation activity is to encourage children to begin conceptualizing quantities in multiple ways. For example the quantity 43 may typically thought of as 4 tens and 3 ones or 43 ones, but it can also be thought of as 2 tens and 23 ones or 3 tens and 13 ones. The activity provides the context for developing children's flexible understanding of quantities.
Video Group 2: Coordinating Units Part II – Becoming Efficient With Reasoning About Sums and Differences By Coordinating Units
This video group provides a detailed description of Part II of the sequence, “Becoming Efficient With Reasoning About Sums and Differences By Coordinating.” The purpose of this part of the sequence is to foster the development of the conceptual basis for solving additive problems involving numbers to 100 by coordinating units of ten with units of one. There are three segments that comprise this set of videos.
Video Segment 2.1
This first segment begins with an overview of Part 2 of the Coordinating Units instructional sequence. It continues by showing how the sequence develops children's ability to reason about sums and differences by coordinating units. The activities discussed show the many different ways children use Unifix cubes to act out "makes more" and "sells some" tasks. These differences reveal the wide range of conceptual understandings of tens and ones within any class at any given time. Through engaging in the tasks and class discussions children make advances in their understanding of sums, differences, and number relationships.
Video Segment 2.2
This segment of Part 2 focuses on children's discussions around the different approaches they use to solve "makes more" and "sells some" tasks. It also introduces a notation method for teachers to record children's solution approaches that allows children to compare different solution methods and to encourage quantitative reasoning.
Video Segment 2.3
The final segment of Part 2
focuses on students' progression to reasoning quantitatively without using Unifix cubes and the role of the anticipation activity in that progression to support students' learning at different levels of reasoning. It also explores the use of partner activities in that process.