t Building Understanding of the Number System Through Hands-On Experiences Marcia Torgrude K-12 Math Specialist

Develop understanding and ideas to promote deeper understanding of the number system. Develop hands-on strategies to help promote understanding of fractions. Use tools to help students work fluently with rational numbers. Experience online tools for the number system

Let’s play! What does this have to do with learning? Where does it fit the common core standards? What about the Standards of Mathematical Practice? Search I Have…Who Has online.

Person facing screen – gives clues Person facing away – guesses the word or phrase

Reasoning Tools Abstract Precision Structure

Standards of Mathematical Practice Persevere Questioning Concrete Modeling

The Practice Standards are descriptions of the fundamental skills needed to “do” mathematics.

Practice Standards describe what it means for students to demonstrate proficiency in mathematics. They are our new “basic skills.” Content Standards are the “what” of mathematics

We must get past the idea of mathematics as a collection of algorithms, steps, or procedures. Just getting answers, although important, is not “doing mathematics.”

Adding Subtracting Multiplying Dividing With Base 10 Blocks

Using Modeling to Make Sense of Mathematical Procedures Modeling addition with Base 10 blocks Race to 100

Using Modeling to Make Sense of Mathematical Procedures Modeling subtraction with Base 10 blocks 302 −

Identify strategies that individuals can use to solve multi-digit multiplication and division problems in sense-making ways Connect concepts to “standard algorithms” Discuss teaching strategies that enhance a child’s understanding

What does multiplication look like using base ten blocks?

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Do you think that using base-10 blocks helps to give meaning to the multiplication algorithm? How? One common concern when using models is that students will not make connections between the concrete models, their representations, and the mathematical concept. Base-10 blocks as an area model emphasize the distributive property and provide a visual representation to the partial products of the multiplication algorithm.

What does division look like using base ten blocks?

How can we use the base ten block array model to help us with division?

Do you think that using base-10 blocks helps to give meaning to the division algorithm? How?

Use of friendly or “benchmark” numbers Partial quotient division Multiplication for division – use what we know

– Activities – Calculation Nation Tens Frame - Grouping and Grazing Adding with base 10 Blocks - _1_t_1.html _1_t_1.html Subtracting with Base 10 Blocks - _1_t_1.html _1_t_1.html Primary Krypto - Product Game - Times Table - illuminations.nctm.org/ActivityDetail.aspx?ID=155http:// illuminations.nctm.org/ActivityDetail.aspx?ID=155

Equivalence Addition Subtraction Multiplication Division

Using Pattern Blocks Using Cuisenaire Rods

Using Arrays

Using Cuisenaire Rods Using Sets

g.html Another Strategy for Division

Equivalent Fractions - Fraction Models - Fraction Game - Fraction Pieces - &from=category_g_3_t_1.html &from=category_g_3_t_1.html Fraction Adding - g_3_t_1.html g_3_t_1.html Fraction Comparing - g_3_t_1.html g_3_t_1.html Fraction Equivalence - g_3_t_1.html g_3_t_1.html Fraction Rectangle Multiplication - g_3_t_1.html g_3_t_1.html

Integers – Charge Model – Linear Model

· Charge Model Use your positive/negative counters to represent the following numbers using at least the number of tiles listed. You can challenge yourself by using more than the minimum number of tiles. Be prepared to share and prove your solution. Ways to build understanding of Integers

· Linear Model Matt earns merits and demerits at his school. One day he earned 3 merits for his math game, 2 demerits for being late to class, 1 merit for being courteous, 5 demerits for arguing with his teacher, and 2 merits for helping another student. If he began the day with 4 merits, how many did he have at the end of the day? Ways to build understanding of Integers

Model the following problems with your counters and sketch your work using a plus sign for positive and a negative sign for negative counters: (-5) (-5) What do you notice? Make some generalizations about the rules for adding integers. Now consider: -3 - (-5) What generalization can you make? Ways to build understanding of Integers

Charge and Linear Model Solve this problem using both methods: He ather started the month with $12. She spent $5 on a game, but realized that she forgot to pay her annual club dues so she wrote a check for $15 because her dad said he would loan her enough money to cover the check. How much does Heather have to borrow from her dad? Ways to build understanding of Integers

How is this different from the way students built their understanding of positive/negative integers in the past? What common core standard have we been working on? What Standards of Mathematical Practice were present during the activity?

Explore Build Add Subtract Multiply Divide

Connecting Number System to Algebra

Illuminations Algebra Tiles NLVM algebra Tiles - l?open=activities&from=category_g_3_t_2.html l?open=activities&from=category_g_3_t_2.html NLVM Scales -Positives l?open=instructions&from=category_g_3_t_2.html l?open=instructions&from=category_g_3_t_2.html NLVM Scales – Negatives l?open=instructions&from=category_g_3_t_2.html l?open=instructions&from=category_g_3_t_2.html Pan Balance - Numbers Pan Balance - Expressions

3 Ideas you will use with your learners 2 Aha’s you had today 1 Question you still have – Please provide your for a response