How to Instruct Place Value & Mental Strategies with Ready Set Math

Sharing is Caring

Module 5: Place Value: Counting Involving Base 10 Units;
Module 6: Addition & Subtraction to 100- Mental Strategies
Post by: Melissa Wilke & Kurt Kinsey

Which comes first, mental math or written algorithm? That is a question… and it seems to be an ongoing contentious point for educators, students, and families.

We believe the development of mental strategies is an important goal in and of itself, but also that it provides the foundation for learning more formal computational procedures with understanding.

Addition and subtraction strategies evolve from knowledge of number sequences and manipulating quantities involving units of 1s, 10s, and 100s. These number ranges remain manageable for mental computation and establish grounded meaning in later learned computation procedures or algorithms used to compute with larger numbers.

The trajectory for this learning involves key ideas in the following stages of teaching and learning:

• Build a foundation of place value through verbal counting by 1s, 10s and 100s
• Count and manipulate quantities by units of 1s, 10s and 100s through the use of place-value-based materials
• Apply knowledge of number relationships for basic facts to an extended range of numbers
• Flexible use of a range of mental strategies that leverage number knowledge and provide a meaningful basis for formal computation

There are two Ready Set Math modules, Place Value: Counting Involving Base-10 Units and Addition & Subtraction to 100: Mental Strategies, that incorporate the learning progression and trajectory of establishing an end goal of mental computation strategies for addition and subtraction involving two-digit numbers and extending to manageable three-digit number computations.

Place Value: Counting Involving Base-10 Units

In the first module, Place Value: Counting Involving Base-10 Units, students and teachers are engaged in learning experiences that involve developing fluency of verbal sequences involving counting by 10s and 100s, forming and manipulating collections that are organized as 1s, 10s, and 100s, and counting them by coordinating the various organizations of the units.

The experiences through a collection of 37 large and small group lessons and 16 independent activities will typically include the use of tangible items that allow for place value groupings to occur (i.e., bundling sticks or place value blocks) or items that incorporate the structure of ten within a number (i.e., mini ten frames).

Addition & Subtraction to 100: Mental Strategies

The learning then shifts in the second module, Addition & Subtraction to 100: Mental Strategies, to a learning progression moving toward the flexible use of mental strategies and formalized computation.

In total there is a collection of 32 large and small group lessons and 18 independent activities.
The module begins first by connecting to the knowledge and use of basic facts within 20 to higher number ranges. From there learning experiences provide students with the opportunity to apply knowledge of units of tens and ones to employ two basic types of mental strategies we regard as Jump and Split strategies.

Mental strategies

• Counting-based strategies (Jump) (e.g., 58 + 24, “58 . . . 68, 78, 80, 82)
• Collection-based strategies (Split) (e.g., 58 + 24 -> 50 + 20 = 70, 8 + 4 = 12 -> 70 + 12 = 82)
• Split/Jump Strategies (e.g., 58 + 24 -> 50 + 20 -> 70 + 8 -> 78 + 4 -> 82)
• Relational-based strategies (Compensation or Transformation) (e.g., 58 + 24 -> 60 + 24 -> 84 – 2 -> 82    -or-    58 + 24 -> 60 + 22 -> 82)

The lessons and activities continue to create learning experiences that extend and refine variations of these mental computation strategies ultimately leading to flexible use of mental strategies to solve addition and subtraction tasks that involve two-digit and manageable three-digit numbers.