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Focal Points- Grades 3 and 4

Using a Journal Article as a Professional Development Experience


Title:           Focal Points- Grades 3 and 4
Author:       Randy Charles and Paula B. Duckett
Journal:      Teaching Children Mathematics
Issue:         April 2008, Volume 14, Issue 8, pp. 466-471.

Rationale/ Suggestions for Use 

The publication, Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM, 2006), shows what mathematics students should know and understand.  It answers the question asked by many educators about what is really important to know in any given year and across grades. One intent of the article, one of a series of four titled Focal Points, is to provide a lens through which the Curriculum Focal Points can be analyzed, viewed and discussed.  It is also to move Curriculum Focal Points beyond curriculum into a discussion of instruction and what it would look like when there are fewer topics of emphasis.  The suggestions below are meant to facilitate this discussion, especially at the classroom level.


  • Copy of the article
  • Chart paper
  • Base 10 blocks


Session One 

As an introduction to Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence, the facilitator could give a short presentation on the publication.

The following resource is a one page summary about Curriculum Focal Points and may be helpful in planning a short presentation.

As an introduction to the discussion on the article, invite participants to read the introductory paragraph on page 466, beginning with, “In grades 3 and 4…”  and ending with “and improve measurement techniques”.

Lead a discussion by asking: “Do you agree that these are the points of emphasis at grades 3 and 4 in your school (or district/ state/ province)? In what way are they the same /different? What are your initial thoughts about the role of Focal Points in bringing about change in your curriculum?

  • Discussion of Multiplication and Division: Divide participants into three groups, each group with a copy of the article.
    • Group A:  First Grade 3 Focal Point: Meaning of multiplication and division.
      All members of the group read pages 466 - 467 from the second paragraph in the section titled, Third Grade Mathematics, ending at the third paragraph on page 467 “is not a Focal Point until grade 4” .
    • Group B:  First Grade 3 Focal Point (continued): Multiplication of multi-digit numbers.
      All members of the group read last paragraph on page 467 beginning with “Third-grade students should have many opportunities…”  to first line on page 468, “student’s strategy was grounded on understanding”.
    • Group C:  First Grade 4 Focal Pont: Quick recall of multiplication and division facts; multiplication of multi-digit whole numbers.

      All members of the group read page 469, section titled Fourth-Grade Mathematics, the 3rd paragraph, 2nd column on page 470, to  “numbers that are less than or greater than one”.
  • Directions for Groups: Read the section of the article assigned. Then discuss and prepare the following for presentation to the whole group:
    • The points of emphasis outlined for your section;
    • Examples of  instructional strategies given  in the examples and diagrams;
    • What you found most interesting about the content and instructional strategies outlined; and
    • What left you wondering.
  • Whole Group Presentations and Discussion:  After  groups make presentations, use the following to guide discussion among the whole group:
    • How do the points of emphasis for multiplication and division, as described in the article, compare to the emphases in your grade 3 and 4 curriculum?
    • If your curriculum placed the same emphasis on multiplication and division as suggested in the article:
      • Would it affect other mathematical concepts and procedures now taught at that grade level? Which ones and why?
      • Would these concepts and procedures be deleted or just receive less emphasis? If so, are you concerned about this?
      • What percentage of the instructional time for mathematics do you suggest would be spent on the following:
        • Multiplication and division in grade 3
        • Multiplication and division in grade 4
        • Do you suggest that the time spent on multiplication in grades 3 and 4 be concentrated or spread out throughout the year. Why?

Session Two 

  • Repeat the activity above for  the other focal points in the grade 3 and 4 mathematics curriculum described  in the article:
    • fractions and fraction equivalence for grade 3;
    • decimals and connections between decimals and fractions for grade 4;
    • geometry in grade 3; and
    • measurement in grade 4.

Next Steps 

  • Basic Facts:
    • It is obvious from the article that we need to strive in grades 3 and 4 for quick recall of multiplication and related division facts. What suggestions do you have for doing this, recognizing developmental needs and the need for varied instructional approaches?
    • What has been your experiences in supporting children’s struggles and successes in attaining quick recall of multiplication and division facts?
    • Has your school/ district introduced some strategies that have worked well for all students?
  • Process Standards:
    • The Curriculum Focal Points are targeted towards content. However the Curriculum Focal Points publication states: “It is essential that these focal points be addressed in contexts that promote problem solving, reasoning, communication, and making connections.” Discuss in your groups and give examples as to how the processes can be integrated into an instructional design for the teaching and learning of the basic facts in grades 3 and 4.
  • Connections:
    • Charles and Duckett, at several points in the article, talk about connections that can be made between number and other areas of the curriculum. On page 471, they state:

      Algebraic connections play an important role at grade 4 as students learn to use their knowledge of identifying and using rules to describe number sequences. They discover that our number system has relationships. For example, the value of each place in a numeral is ten times more (multiplied by 10) than the value of the place for the numeral to the right. Using place-value relationships and patterns for whole numbers, student scan develop numeration concepts, relationships, and terminology for decimals.
      • Discuss the above excerpt in relation to how patterns and relationships help children develop decimal concepts.
      • Has making this connection been a part of your instructional plans? In what way?

Note: Since one tenet of Curriculum Focal Points  is that of developing a cohesive curriculum, in which ideas develop across the grades, it would be worthwhile to have participants in the discussion of the above article also read  and discuss the following articles:

Connections to Other NCTM Publications  

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