Appendices
A1
5Math Talk Norms to Facilitate Discussion.
- Agree/Disagree with ideas and not the person.
- Allow people to speak for themselves and allow for appropriate think time.
- It’s ok to make mistakes and revise our thinking.
- Make sense of mathematics by asking questions to clarify misconceptions.
A2
Whole Number Prompts: Each placement prompt can be given with or without labeled intervals while comparison is encouraged throughout.
- In Relation to Figure 7: Express the following integers as vectors: -7,19,4,12,-2,-5,9,5
- In Relation to Figure 8: Positive Number Pairs for Comparison: 3&5, 6&1, 18&8…Students will be asked to compare each pair using the greater than or less than symbol.
- In Relations to Figure 9: Positive and Negative Number Pair: -3&5, 3&-5 … These can be altered to mimic the pairs previously covered, just changing the sign. I want to choose integer pairs that will challenge the idea of magnitude. Students will be asked to compare each pair using the greater than or less than symbol.
- In Relation to Figure 10: Both Negative Integers. Students will be asked to compare each pair using the greater than or less than symbol.
Rational Number Prompts
- Problem sets should include variations of Figures 16 through 18 with different partitions as well as omitted information.
- In Relation to Figure 19: Improper Fraction Placement: 24/9,21/4,10/3,56/6,32/5,34/7,9/8,11/2
- Rational Numbers Placement with Different Denominators/Signs:
- 3/8,_2/7,1/3
- 5/3,7/4,1/7
- (-4)/7,7/4,(-7)/4
Decimal Prompts
- In Relation to Figure 20: Students will be asked to “zero in” on the following decimals by
creating a series of number lines for each place value.
- 923. First, placing 5, then 5.9, then 5.92, then 5.923
- 23. First, placing 1, then 1.2, then 1.23
- 211. First, placing 8, then 8.2, then 8.21, then 8.211
Combined Prompts
- As an extension to the above prompts, students will be asked to place multiple representations of numbers on the number line. This will allow for deeper understanding and help solve the siloed understanding of numbers.
A3
Common Core State Standards and Standards for Math Practice
CCSS
6.NS.C.5 - Understand that positive and negative numbers are used together to describe quantities having opposite directions or values
6.NS.C.6 - Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
7.NS.A.2.B - Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
7.NS.A.2.D - Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
SMP
MP1 – Make sense of problems and persevere in solving them.
MP3 – Construct viable arguments and critique the reasoning of others.
Comments: