Landmark Numbers and Other Post-March Topics

By now parents of children grades 1-8 should have received a brochure to “keep you updated about your children’s math instructional program.”

The first reaction of many elementary parents was not about content but rather “why was this sent in the mail instead of in my child’s backpack like everything else?”  Although it makes sense in the middle school environment, elementary parents are used to and support the frugality of sending home only the most dire necessities in the mail. 

Some other observations:

• Information regarding Grades 5 and 6 were combined, as were 7 and 8. With the poor math scores and problems facing our Middle School math students, certainly each grade warrants it's own individual curriculum.
  
  
• No specific examples of math are shown using numbers and symbols.
  
  
• Graphics, our school district’s mission statement and a listing of Board of Ed members take up a section and a half of the 4 section pamphlet or 37% of the available space. If you add in the section-long generalized message from Assistant Superintendent of Curriculum and Instruction Mrs. Hodrinsky, roughly 62% of this update is devoted to non-specific information about math curriculum.
  
  
• Web-sites are given, including a glossary from NYS, http://www.emsc.nysed.gov/3-8/pk-8glossary.doc, to cross-reference the Key Vocabulary Terms listed, in the event your memory has failed on exactly what an addend, pictograph, numerator or denominator is.  The first sentence of the document starts with “This Glossary, intended for teacher use only.”  

The Grade 3 vocabulary guide includes “landmark numbers.” This phrase is not referenced in the NYS mathematics glossary or in a colorful, child and parent friendly general math dictionary http://www.amathsdictionaryforkids.com/.  

A Google search on “landmark numbers” brought up TERC Investigations-related materials, and this lengthy explanation.

Bill Quirk’s guide TERC Hands-On Math: The Truth is in the Details  An Analysis of Investigations in Number, Data, and Space  gives a  shorter definition:   Landmark numbers are 5, multiples of 10, and multiples of 25, also known as anchors.

Most of us could have taken an educated guess that 79 or 147 weren’t going to be a landmark number but 50 or 100 probably would.  However, the point of these guides is to improve home/school communication.  

Unfamiliar terms need to be clearly and easily defined.  Also, special care needs to be taken to familiarize parents with unusual and idiomatic phrases referenced only by the Investigations math programs.

Parent guides should be one-stop, easily understandable references, not starting points of other searches. Textbooks usually provide definitions and examples of terminology used and will hopefully be coming home in a backpack near you soon.

Until then, perhaps new brochures will be created that will include definitions of essential vocabulary and examples that support the descriptions of math.

Math Content

Question: What is the purpose of landmark numbers in Investigations? Why do children need to use them? What are ways they are taught, developed, and discussed in the Investigations program?

Janis Freckmann
Elementary Mathematics Coordinator
Milwaukee Public Schools

Note: This response draws mainly from the About the Math in Grade 2: Putting Together, and the Grades 3, 4 & 5 Landmarks units.

Answer: An important part of students' mathematical work in the elementary grades is building an understanding of the base ten number system. Part of becoming familiar with that system is learning about the relationship of numbers to important landmarks-numbers that are familiar landing places, that make for simple calculations, and to which other numbers can be related, such as 10, 100, 1000, and their multiples and factors. Familiarity with these landmark numbers is a cornerstone of good number sense-what one unit describes as involving "a deep understanding of numbers, their characteristics, their place in the number system, and their relationships to one another." (Grade 4, Money, Miles, and Large Numbers, page 9.)

"When solving real problems, people with well-developed number sense draw on their knowledge of these important landmarks. For example, think about how you would solve this problem, in your head, before you continue reading:

If there are about 25 students in a class and 17 classes in our school, about how many students are there altogether?

Many people would use their knowledge that there are four 25's in every 100 to help them solve this problem mentally. Rather than multiplying 17 by 25, they will think something like this: "There are four 25's in 100; there are eight in 200, 12 in 300, 16 in 400-and one more 25 makes 425." (Grade 4, Landmarks in the Thousands, Page I-18.)

Efficient strategies to solve computation problems often depend on an understanding of how to use landmark numbers and in order best to find the final answer.

Those still interested can click here for the full TERC Investigations explanation of Landmark numbers