Math Trailblazers Skills
Fifth Grade Mastery by Month
Topics may be introduced earlier, but the following is the month they should be mastered!
List of ongoing activities to be completed weekly: (Once skills appear, continue to do activities related to each)
- Problem Solving: Solve addition, subtraction, multiplication, and division problems using whole numbers, decimals and fractions. Include elapsed time and money.
- Place Value: Group tenths to thousandths and whole numbers through millions.
- Facts and Algorithms: Practice with objects, pictures, and paper and pencil all basic facts and algorithms for whole numbers, fractions and decimals.
MONTH 1: AUGUST
Unit 2: Big Numbers (Complete: 1,5,6, 8) &
Unit 4: Division and Data (use as a Review) (Omit lesson 1,2,6,7)
*Must complete “FACTS I KNOW ASSESSMENT” – through 9x9 including division facts that accompany them.
Students will:
- Place Value: Recognize that in multi-digit whole numbers, a digit in one place represents 10 times what it represents in the place to its right, and 1/10 of what it represents in the place to the left. (5.NBT.1)
- Division: Find whole number quotients of whole numbers with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and /or relationship between multiplication and division. (5.NBT.6)
- Write and Interpret Numerical Expressions: Use parentheses, brackets or braces in numerical expressions, and evaluate these with symbols. (5.OA.1)
- Write and Interpret Numerical Expressions: Write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them. (5.OA.2)
- Multiplication: Fluently multiply multi-digit whole numbers using standard algorithms. (5.NBT.5)
MONTH 2: SEPTEMBER
Unit 3: Fractions and Ratios (Omit lesson 1)
Unit 5: Investigating Fractions (Omit lesson 1)
Students will:
1.Addition and Subtraction of Fractions: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (5.NF.1)
2.Addition and Subtraction of Fractions: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e/g/, by using visual fraction models or equations to represent the problem. (5.NF.2)
3.Geometry: Use a pair of perpendicular lines, called axes, to define a coordinate system. Graph on a Cartesian plane. (5.G.1)
4.Geometry: Represent real world and mathematical problems by graphing points in the first quadrant. (5.G.2)
MONTH 3: OCTOBER
Unit 7: Decimals and Probability (Omit 9, & 10)
Students will:
1. Decimals: Read, write, and compare decimals to thousandths. A. Read and write decimals to thousandths using bas ten numerals, number names, and expanded form. B. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of the comparisons. (5.NBT.3)
2.Decimals: Use place value understanding to round decimals to any place. (5.NBT.4)
3.Decimals: Add, subtract, multiply and *divide decimals (to hundredths) using concrete models and equations. (5.NBT.7)
4.*Decimals: Explain patterns in the number of zeros of the product when multiplying by powers of 10, and explain patterns in the placement of the decimal points when a decimal is multiplied or divided by a power of 10. (5.NBT.2)
MONTH 4: NOVEMBER
Unit 6: Geometry (Do all lessons)
Students will:
- Geometry: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. (5.G. 3)
- Geometry: Classify two-dimensional figures in a hierarchy based on properties. (5.G.4)
MONTH 5: DECEMBER
Unit 8: Applications: (Complete Mid-year test only)
Unit 9: Connections to Division (Omit 3, 6)
- Division: Find whole number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and /or relationship between multiplication and division. (5.NBT.6)
MONTH 6: JANUARY
Unit 11: Number Patterns, Primes and Fractions (Omit 7, 8)
Unit 12: Using Fractions (Omit 6, Lesson 7 is Homework)
- Fractions: Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. (5.NF.3)
Month 7: FEBRUARY
Finish Unit 12: Using Fractions
Unit 13: Ratio and Proportions
- Fractions: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction (including mixed numbers). A. Interpret the product as a part of a partition. *B. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths. (5.NF.4)
- *Line Plot: Make a line plot to display a data set of measurement in fractions of a unit. (5.MD.2)
Month 8: MARCH
Finish Unit 13: Ratio and Proportions (Omit 2)
- *Fractions: Interpret multiplication as scaling (resizing), by: a. comparing the size of the product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. B. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying by a fraction less than 1 results in a product smaller than the given number. (5.NF.5)
- *Fractions: Solve real-world problems involving multiplication of fractions and mixed numbers.(5.NF.6)
- *Fractions: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (5.NF.7)
- *Patterns and Relationships: Generate and graph two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. (5.OA.3)
Month 9/10: APRIL/MAY
*1. Conversions: Convert among different sized standard measurement units within a given measurement system, and use these conversions un solving multi-step, real world problems.(5.MD.1)
*2.Volume: recognize volume as an attribute of solid figures and understand concepts of volume measurements. (5.MD.3)
*3.Volume: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (5.MD.4)
*4.Volume: Relate volume to the operation of multiplication and addition and solve real word and mathematical problems involving volume. (5.MD.5)
*Items with a *are not covered in depth in Trailblazers and will require additional resources.
*****Units 1, 8, & 10, 14, 15, 16 have been omitted.
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DraftMarch 2, 2011