In accordance with the National Council of Teachers of Mathematics Principles and Standards for School Mathematics, the Curriculum Focal Points (NCTM 2000, NCTM 2006) and the Common Core Standards for Mathematics, *Math Trailblazers* students are expected to develop proficient strategies for solving multidigit multiplication and division by the end of fourth grade.

### Developing Math Facts

In Grade 4, students review and are assessed for fluency on their addition and subtraction facts. Students have been developing strategies for solving these facts since their early years and should have gained fluency.

A systematic review of the multiplication and division facts begins early in the year. Students review multiplication facts to maintain or gain fluency and also work on developing fluency with the division facts. Students review strategies for learning the facts in small groups, practice the facts in the Daily Practice and Problems (DPP), and then take a short quiz on the fact families and the multiplication facts. Students track their own progress by circling the facts they know on their Multiplication Facts I Know charts. A Multiplication Facts Inventory Test is included at this point in the curriculum based on recommendations from research. Students update their Multiplication Facts I Know charts and make a new list of any facts they still need to study. In line with research recommendations, students’ practice is focused just on these facts. The test is presented as a diagnostic tool to develop “targeted forms of practice” for those facts students are still having difficulty with. Students are encouraged to develop efficient strategies for these facts, as opposed to just memorization.

There is a systematic study of the division facts in Grade 4, the goal being for students to develop fluency with the division facts by the end of the year. The main strategy for learning the division facts is to use the related multiplication facts. Therefore, expectations for fluency have been delayed until students have reasonable fluency with the multiplication facts. Students use fact families to connect the multiplication facts to the division facts.

**Distributed Facts Practice.** Following research recommendations, students study and practice small groups of facts that can be found using similar strategies. See Figure 1 for distributed facts practice in Grade 4.

**Figure 1:** Distributed Facts Practice in Grade 4