2. By teaching our students processes without providing them with the opportunity to make meaning, students have a hard time applying the skills taught. When students are given the opportunity to create their own understanding in authentic situations, learning takes place on a deeper level. Numbers without meaning mean nothing. Students are less likely to catch their mathematical errors if they are unable to identify answers that don’t make sense. We’ve learned a lot about learning styles and we now recognize that students learn in different ways and at different rates. By exploring multiple perspectives to solving a problem, students are more likely to find one that works and makes sense to them.

3. In addition to using the term “apply algorithm” to solve problems, the new standards state that students should “generate strategies” to solve problems. The year a new operational skill is introduced, students will be taught to generate strategies for that skill. The algorithm for that skill will be taught the following year, when students have developed an understanding of the concept.

4. 2nd Grade- 2-2.7Generate strategies to add and subtract pairs of two-digit whole numbers with regrouping. 2-2.8Generate addition and subtraction strategies to find missing addends and subtrahends in number combinations through 20. 3 rd Grade- 3-2.3 Apply an algorithm to add and subtract whole numbers fluently. 3-2.10 Generate strategies to multiply whole numbers by using one single- digit factor and one multidigit factor. 4 th Grade- 4-2.3Apply an algorithm to multiply whole numbers fluently. 4-2.5Generate strategies to divide whole numbers by single-digit divisors. 5 th Grade- 5-2.2 Apply an algorithm to divide whole numbers fluently. 5-2.8 Generate strategies to add and subtract fractions with like and unlike denominators. 1 st Grade- 1-2.8Generate strategies to add and subtract without regrouping through two-digit numbers.

5. Opportunities to think through and express their mathematical ideas Discussions that cause them to consider the mathematical thinking of others Questioning that inspires them to examine mathematical concepts on a deeper level Supports real world problem solving skills Fosters conceptual learning in context, rather than isolated skill and drill.

6. promotes flexible thinking equips students with a variety of strategies through peer sharing risk taking fosters student directed learning community

7. Non-negotiables Problems designed to promote flexible thinking Time for students to think through their strategies Time for TALK and strategy shares Safe environment to encourage risk taking

8. Sample Notebooking Guidelines 1. Date your entry. 2.Write out the problem or question in your notebook. If your teacher gives you a copy of the problem, glue it into your notebook neatly. 3.Place a box around your drawings. All drawings must be explained with words, too. 4.Show your best thinking neatly and legibly. This takes time! 5. Prove your answer. 6. You must check your work!

9. The Acrobat Bears are stuffed bears. Zeke Bear is the tallest. Yolanda is 3 inches shorter than Zeke. Wanda is 3 inches shorter Yolanda. Un is 3 inches shorter than Wanda, and Timothy is 3 inches shorter than Un. Timothy Bear is 6 inches tall. If you stood on top of each other, how high would the bear tower be?