Chapter 10 - Developing Whole Number Place Value Concepts (Important Place…
Chapter 10 - Developing Whole Number Place Value Concepts
Extending Number Relationships to Larger Numbers
- focusing on a quantity in terms of its parts has important implications for developing number sense as well as operation sense
- the size relationship one number has with another number. Is it much larger, much smaller, close or about the same? -ELLs can modify by using prompts that are similar to each other and using visuals for help with questions
- encourage students to see large numbers in the world around them. Turn numbers of students, minutes in school, cartons of milk into interesting graphs, stories & make up problems with the students
Approximate numbers and rounding
- most familiar estimation is rounding. Students in grade 3 are expected to understand rounding numbers. To round a number means to make it a compatible number (167 to 170)
Important Place Value Concepts
Base-ten counting by ones
We want students to see 53 as 53 ones but also as 5 groups of ten and 3 extra ones. Students must construct this relationship on their own, they can't just told it
Base-ten with words
The way we say a word "fifty-three" is also connected with grouping by tens concept. It connects 5 tens and 3 ones. For ELLs, choose one base-ten concept and consistently use
Base-ten with place-value notation
Language plays a key role in understanding these groupings. The symbolic scheme we write numbers in (left to right, large then small). All three base-ten models work together
Physical models help students get the idea of "a ten" as a single unit and as a set of 10 units. Make the model proportional for students to see the 10 is physically 10 times bigger than the one.
Non proportional models are not used for introducing place-value concepts
Extending Base-Ten Concepts
When students enter 3rd grade they are expected to know that 1000 is more than just 1000 ones, but is 100 tens, 10 hundreds and one 1000.
Use base-ten riddles to help build the understanding and relationship of multiple ways to solve base-ten concepts
Oral & Written Names for Numbers
Give students mixed arrangement of base ten materials and have them tell you base-ten name and standard name. Vary the next problem by changing one item. Biggest challenge with 3 digit is the numbers involving no tens, 703.
proportionally make manipulative larger size for students to visually see thinking.
Students struggle even more with 4 digit numbers than 3 digit numbers so don't assume they will be able to generalize
Patterns & Relationships with Multi-digit Numbers
tool for developing ten-structured thinking. Students will need for help exploring invented strategies. Very useful when exploring patterns
Its useful to realize numbers can be broken into 'familiar' numbers to help with the operations. Deal with familiar numbers first then smaller leftover pieces
Numbers Beyond 1000
Conceptualizing large numbers
Using visuals for larger numbers are sometimes to hard to understand. Instead use the imagination and interests to build questions of relevance
Extending place-value system
multiplicative structure must be generalized. Oral and written patterns must be duplicated for every 3 digits (??)
Students must understand the system does have a logical structure, its not totally arbitrary