Building number sense through mapping devices – 2 nd Grade

1. Kari McLaughlin, Tameka Gordon-Sneed & Keri Davis, Jill Baker – District Numeracy Coaches Building number sense through mapping devices –2nd Grade K-2 CCSS MNPS District Training June 10 – 14, 2013

2. Building Number Sense is Essential for Student Learning • Number sense refers to a person’s general understanding of number and operations and the ability to handle daily life situations that include numbers. This includes the ability to develop useful, flexible and efficient strategies (i.e. mental computation) for handling numerical problems. - Howden, 1989; McIntosh, Reys & Reys 1992, etc. • Students who participate in well-designed activities are more likely to develop number sense than students who receive instruction focusing on the development of standard written algorithms and computation proficiency. - Sowder, 1941; Reys 2001 • In this session, we will look at instruction that is fostering number sense.

3. Early Numeracy Strategies • Developing spatial relationships involving hands-on experiences (i.e. provide sensory input that helps students develop mental imagery) • Focusing on the meaning of sets in the context of problems • Developing visual cues such as dot cards and patterns on the die help students see relationships. • Building mental imagery expands children’s ability to think in flexible ways. • Recording students’ ideas as they share them can reinforce concepts and help students make the connection between the concrete items and the abstract numbers.

4. Early Numeracy Strategies • Solving problems involving joining, separating, grouping, and sharing helps students see how sets come together and are taken apart. • Counting and showing objects to 120 helps students to hear the number pattern and see quantities. • Counting forward and backward • Ordering/sequencing sets, pictures, and numbers from least to greatest • Matching numerals to objects • Being exposed to part/whole relationships • Showing students sets and asking them to make estimations of the quantities.

5. Numeracy Activities – Mapping Devices • Subitizing – Pattern recognition • Ten Frame Recognition (Math Racks) • Part-Part Whole • Number Line (Number Paths) • Number Chart

6. Subitizing • What is subitizing? • “Instantly seeing how many” Pattern or decomposition of the group Basis of number sense • Where do we use our knowledge of grouping in real- world situations? • IT’S TIME TO PRACTICE! • http://www.ircsd.org/webpages/dyoung/subitizing.cfm • Together let’s brainstorm questions we can ask students to advance their thinking. • What content and practice standards are met by subitizing?

7. Ten Frames • Look at 10 Frames • How will subitizing aid in concepts taught using the ten frames? • When do we use a Ten Frame? • Addition, subtraction, part -part -whole, placement • Decomposing numbers to10 • 20 Frame-Why use it? • http://illuminations.nctm.org/ActivityDetail.aspx?ID=75

8. Frames and Mats • Let’s take a look at the 40 Frame • What is the most difficult standard that is taught in the 2nd grade? • REGROUPING • Link for games

9. Math Racks • What is a Math Rack? • The original arithmetic rack, also known as a Rekenrek, was developed by Adrian Treffers, a mathematic curriculum researcher, at the Freudenthal Institute in Holland.  It was designed to support the natural mathematical development of children’s addition and subtraction strategies as well as encourage and enhance children’s strategic mathematical thinking. • Though it resembles an abacus it is not based on place value columns and it is not used in that way.  It is comprised of two rows of tens, each broken into two sets of five.  This allows the children to ‘privilege 5’ and ‘think 10’ which leads to better number sense, efficient calculation and quick recall of math facts.

10. Math Racks • Let’s create a Math Rack! • How can the math rack be used to teach Sets/Groups Sums to 20 Foundation for multiplication • Greater than/less than • Let’s take a look at some other types of math racks and strategies? • What content and practice standards are met by using ten frames and math racks?

11. Part Part Whole • How many different ways can you represent part- part whole relationships?

12. Part-Part Whole with Number Line

15. Number Bonds

17. What content and practice standards are met by using the part-part whole model?

18. Number Line • Addition/Subtraction Fluency Example: Run Races on the number line using dice. • Comparing numbers, odd, even, repeated addition and patterns – basis for multiplication • PLAY THE GAME – GUESS MY NUMBER • What content and practice standards are met by subitizing?

19. Open Number Line

20. Number Chart 0-99 chart vs.100 chart What do you think?

21. Activity “Number destination” Essential questions answered: • How can different combinations of numbers and operations be used to represent the same quantity? • How can we use skip counting to help us solve problems? • How does using ten as a benchmark number help us add or subtract?

22. Activity “I Spy A Number”

23. Wonders of the Number Chart Activity 3: Locating Number Neighbors Have students use a blank number chart. Have a student select a number from 0 to 99. Everyone must find where the number belongs on the number chart. Students must then write the number neighbors. A number that is one more than, one less than, ten more than and ten less than the selected number. Continue until the chart is filled in. Activity 4: Name Patterns Have students use a blank number chart. Have students begin writing their first name placing one letter in each box. They continue writing their first name until they reach the end of the chart. Next, have students shade in the first letter of their name. They must shade in all of the first letters of their name every time they wrote their name. Have students find other students who have the same shaded pattern. Have students examine the patterns together and discuss what they observe. The shaded patterns are the multiples of 3, 4, 5, 6, 7, 8, 9, 10, etc. depending on how many letters are in the students name.

24. What content and practice standards are met by using a number line or number chart?

25. Closing • Dueling Charts