Basic Facts and Operations By Jessica Rodriguez

Number Operations Addition Subtraction Multiplication Division

Big Ideas Addition and subtraction are connected. –Ex.: = 11 and 11 – 6 = 5 Multiplication and division are connected. –Ex.: 7 x 5 = 35 and 35/ 7 = 5 Models can be used to solve problems for all operations. Problems in context focus children on finding meaning and mathematical thinking.

Teaching Addition and Subtraction Using Contextual Problems Using Model-Based Problems Comparison Models The Order Property and the Zero Property

Using Contextual Problems Connect the problems to children’s lives. –Ex: How many blocks long is your body? How many more blocks long is your body than your partner’s body? Children use words, pictures, and counters to solve problems. Provide children with access to a variety of manipulatives. Introduce symbols after children understand and have solved the problem. Focus on one or two problems in a session, rather than pages of problems.

Using Contextual Problems What are the advantages of teaching addition and subtraction through contextual problems?

Using Contextual Problems What are some examples of contextual problems you can use in “real life?” In your classrooms, with your children, etc.

Using Model-Based Problems Join or separate using blocks or counters. 3+5= 8 or 8-5=3 Use a number line. 3+5= 8 or 8-5=3 0_1_2_3_4_5_6_7_8 To add, start on 3 and hop up five.

Using Model-Based Problems Teach subtraction as “think- addition” Examples: What goes with 5 to make 8? 5+ □ =8 is the same as 8-5= □

Using Model-Based Problems How can models help develop the connection between addition and subtraction?

Comparison Models Involve comparing two different sets of numbers. (Does not involve putting parts together or taking parts away) Example: How many more is 9 than 3?

Comparison Models More examples: How much taller is Tania than Kara? Sam picked 6 apples. Shari picked 8 apples. How many fewer apples did Sam pick? What are some real-life examples kids could compare in class?

The Order Property and the Zero Property Order Property: You can add in any order. Example: 9+5 = = Zero Property: Adding or subtracting zero does not change the value. Example: 0+5 = = 5

The Order Property and the Zero Property How would you help children develop an understanding of these properties?

Teaching Multiplication and Division Using Contextual Problems Use Model-Based Problems Teach Properties

Using Contextual Problems Multiplication is repeated addition (counting groups of the same size) Ex: There are 8 rows of students and 5 students in each row. How many students? 8x5 = Division is repeated subtraction (removing groups of the same size) Ex: There are 40 students divided into 8 rows. How many students in each row? 40/5 =

Using Contextual Problems What are some other examples of contextual problems with multiplication and division?

Use Model-Based Problems Use counters, blocks, rows, number lines (skip counting), graph paper, etc. Consider the hearts counters and the rectangle an array…

Use Model-Based Problems Why use models over memorization when introducing the operations of multiplication and division?

Teach Properties Multiply in any order –6x5 = 5x6 The role of 0 in multiplication –6 x 0 = 0 The role of 1 in multiplication and division –4 x 1 = 4 and 4/1 = 4 The distributive property –6 x 9 is the same as (6x5) + (6x4)

Teach Properties Why is it important for children to learn the properties of multiplication and division?

Memorizing the Facts…

What is the difference between “drill” and “practice?” Drill: Drill is repetitive non- problem based activity. Practice: problem based experiences where children encouraged to develop flexible and useful strategies that are personally meaningful

When is using drill in the classroom appropriate? Drill is appropriate for practicing strategies that the student knows, understands and likes, but doesn’t use automatically Drill is not appropriate for introducing new concepts and memorizing facts the students do not understand

Question… Why do we avoid “drilling” students on new concepts?

Addition and Subtraction Strategies… Some strategies For Addition: –One more than and two more than –Facts with zero –Doubles –Near doubles –Make-Ten facts Some Strategies for Subtraction –Think-Addition –Build up through 10. Ex Change 13 to 14 and 9 to = 4, so 13- 9= 4 –Back down through 10. Ex: 14-5 Take 4 away from 14 to get to 10. Take 1 more off to get to 9

Multiplication and Division Strategies… Doubles (2x2, 2x3, 2x4, etc) –Double the number multiplied by 2 Five Facts Zeros/Ones Nifty Nines –See page 178

Question… What is the benefit of teaching these strategies in learning basic math facts?