1. Critical Components of a Math Class By Brandi Crouch

2. 5 Steps to a Balanced Math Program by Larry Ainsworth and Jan Christinson 1. Computational Skills – Math Review and Mental Math 2. Problem Solving 3. Conceptual Understanding 4. Mastery of Math Facts 5. Common Formative Assessments

3. Step 1: Computational Skills  Math Review  Mental Math  “Number sense encompasses a wide range of abilities, including being able to make reasonable estimates, think and reason flexibly, make sound numerical judgments, and see numbers and useful. Students with number sense have good numerical intuition,” Marilyn Burns, 1999.

4. Math Review  3-5 problems, teacher selected  Math Review Quiz on Fridays

5. Math Review  3-5 problems, teacher selected  Math Review Quiz on Fridays

6. Mental Math  3 problem computational workout for the brain  5 minutes of class immediately after math review  Bar diagrams; part-part-whole relationships  Mental Math in the Primary Grades  Mini-lesson then reinforce in centers  Most commonly skipped to “fit more in”, but grave consequences

7. Mental Math themes (K-2)  One more/one less  Counting by 2s, 5s, and 10s  Anchors of 5 and 10 (five frames and ten frames)  Doubles  Part-part-whole relationships (fact family groups)  Number facts (addition and subtraction)  Math vocabulary  Measurement concepts

8. Mental Math Themes (3-5)  Number facts (+, -, x, ÷)  Combining operations  Multiplying/dividing by 10, 100, 1000  Number properties  Math vocabulary  Fractional parts  Skip-counting (3s, 5s, 9s, and so on…)  Part-Part-Whole relationships  Fraction-decimal equivalency  Measurement concepts

9. Step 2: Problem Solving  Focus on process and on communication  “Writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas – all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions, and their feelings about the content they’re learning,” - Marilyn Burns, 2004.

10. Problem Solving  Gradual release of responsibility Model, model, model Cooperative groups Pairs Individual  Choose problems that allow them to apply the math they are currently learning

11. Problem Solving  The end goal in grades 3-5 is: “for them to be able – before the end of the school year – to solve independently a multistep problem and to communicate verbally and in writing the process they used.” p. 33 of Upper Elementary Grades.  The end goal in the primary grades is: “to solve independently a two-step or a multistep problem and to communicate verbally (kindergarten) and in writing (grade 1 and grade 2) the process they used, p. 35 of Primary Grades.

12. Step 3: Conceptual Understanding  Concept vs. procedure  Big Ideas: diving deep rather than skimming the surface  Investigations  Introduce, explore, explain, explore, evaluate

13. Step 4: Mastery of Math Facts “Memorization plays an important role in computation. Calculating mentally or with paper and pencil requires having basic number facts committed to memory. However, memorization should follow, not lead, instruction that builds children’s understanding. The emphasis of learning in mathematics must always be on thinking, reasoning, and making sense,” - Marilyn Burns, 1999.

14. Math Facts “Fortunately we know quite a bit about helping children develop fact mastery, and it has little to do with quantity of drill or drill techniques. Three components or steps to this end can be identified: 1. Help children develop a strong understanding of the operations and of number relationships. 2. Develop efficient strategies for fact retrieval through practice. 3. Then provide drill in the use and selection of those strategies once they have been developed.” - Van De Walle, 2004.

15. Math Facts  Pre-assess  Teach patterns  Provide daily practice  Assess  Mrs. Hutcheson’s boot camp Mrs. Hutcheson’s boot camp

16. About Timed Tests “Teachers who use timed tests believe that the tests help children learn basic facts. This perspective makes no instructional sense. Children who perform well under time pressure display their skills. Children who have difficulty with skills, or who work more slowly, run the risk of reinforcing wrong practices under pressure. Also, they can become fearful about, and negative toward, their mathematics learning,” - Burns, 1999.

17. Step 5: Common Formative Assessment  Collaborative  Frequent  DCAs too short, consider adding 5 more questions that your grade level develops together

18. Sample Schedule WeekMonTueWedThurFri 1 Math Review – 20 Prob. solving – 30 Concept – 15 Math Facts* – 5 Math Review – 20 Mental Math – 5 Prob. solving – 20 Concept – 20 Assign h.w. – 5 Math Review – 20 Mental Math – 5 Prob. solving – 15 Concept – 25 Assign h.w. – 5 Math Review – 20 Mental Math – 5 Prob. solving – 15 Concept – 25 Assign h.w. – 5 Math Review Quiz – 30 Concept assess – 20 Centers – 20 2 Math Review – 20 Prob. solving – 30 Concept – 15 Math Facts* – 5 Math Review – 20 Mental Math – 5 Prob. solving – 20 Concept – 20 Assign h.w. – 5 Math Review – 20 Mental Math – 5 Prob. solving – 15 Concept – 25 Assign h.w. – 5 Math Review – 20 Mental Math – 5 Prob. solving – 15 Concept – 25 Assign h.w. – 5 Math Review Quiz – 30 Concept assess – 20 Centers – 20 3 Math Review – 20 Prob. solving – 30 Concept – 15 Math Facts* – 5 Math Review – 20 Mental Math – 5 Prob. solving – 20 Concept – 20 Assign h.w. – 5 Math Review – 20 Prob. solving – 15 Concept – 30 Assign h.w. – 5 DCA/BAReview test results