1.1 Review from Comparing Bits and Pieces Inv. 3

Lets be Rational

Standard / Also Covered in / Unit Test / State question
A / M / T
6.NS.1 / Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Investigation 3,4 / 2
12 / 8 / 2013 pg. 3
2013 pg. 25
6.NS.2 / Fluently divide multi-digit numbers using the standard algorithm. Investigations 3 / Comparing Bits Inv. 4
Decimal Ops. Inv. 1,3,4
6.NS.3 / Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Investigations 1, 2, 3and 4 / Comparing Bits Inv. 3
Decimal Ops. Inv. 1,2,3,4
6.NS.4 / Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Investigations 1, 2, 3, and 4 / Prime Time Inv. 2, 4
Comparing Bits. Inv. 1,2,3
6.NS.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. Investigations 1 / Comparing Bits Inv. 3
6.EE.1 / Write and evaluate numerical expressions involving whole-number exponents.. Investigations 4 / Prime Time Inv. 3,4
6.EE.2c / Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).. Investigation 2 / Prime Time Inv. 4
Covering Inv. 1,2,3,4
Variables Inv. 3,4
6.EE.3 / Apply the properties of operations to generate equivalent expressions.. Investigation 4 / Prime Time Inv. 1,4
Covering Inv. 1
Decimal Ops. Inv. 3
Variables Inv. 4
6.EE.4 / Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).. Investigation 4 / Covering Inv. 4
Variables Inv. 4
6.EE.5 / Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.. Investigation 4 / Variables Inv. 4 / 4
5
6
7
6.EE.6 / Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Investigation 4 / Covering Inv. 1,2,4
Variables Inv. 3,4
6.EE.7 / Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. .Investigations 4 / Variables Inv. 3,4 / 2013 pg. 8

Unit Notes:

Inv. 1 Sums of fractions and decimals

1.1  – Review from comparing bits and pieces inv. 3

Estimating sums of fractions, decimals and then fractions and decimals mixed

Discuss strategies used to estimate

Overestimate, underestimate discussion in summarize is important for 1.2

1.2  – Overestimating and underestimating in context

1.3  - Using area to get equivalent fractions to add and subtract - easier level since denominators are all mult. of 2. Used to build idea of getting common denominators

1.4  – Might want to share regrouping strategies for multi-digit whole numbers before problem so students can make connections to regrouping with fractions. Share algorithms at end. Algebraic ideas are introduced but no formal algebra

Inv. 2 - Fraction Multiplication

2.1 – Share different methods for multiplication – Part E develops standard algorithm – needed in later problems

2.2 – Challenging visual models – will take some time. Develop understanding of when multiplying by a fraction makes your number larger/smaller

2.3 - Compare different algorithms and have discussion about which and better and when

Inv. 3 – Division of fractions

3.1 – Visual strategies – focus on meaning of division – strategy of getting common denominator to then divide numerators

3.2 – Whole # divided by fraction – Continue visual model. If student start make connections to shortcuts have them explain and connect to the visual model

3.3 – Fraction divided by a whole #

3.4 – Practice to develop algorithm – share similarities between different algorithms students have developed

Inv. 4 – Practice with fractions through use of fact families. Preparing for equation solving.

4.1 Addition fact families and fraction practice

4.2 Mult. Fact families and fraction practice

4.3 Mixed practice in context, students decide which operation to use. Spend some time on the distributive property discussion.