California, Mathematics Concepts Found in Science Explorer, Focus on Earth Science Textbook (Grade 6) 1 11 Describe the layers of the Earth 2 p. 59-61 Draw a circle with a specified radius or diameter Collect and display Organize and describe distributions of using line graphs Explain how a geologist uses seismic waves to locate an earthquake s epicenter 2 p. 75 Read and interpret real-life displayed on graphs Read and interpret a seismograph record for an earthquake 1
3 p. 82 Discover and extend mathematical/geometric patterns Plot points on a map using latitude and longitude Interpret on the locations of earthquakes and volcanoes to find patterns 4 p. 117 Collect, organize, represent sets in table form Apply formulas to real-life problem-solving Conduct an experiment to measure the density of different materials 4 p. 132 Use Venn Diagrams to illustrate intersection and union of sets Compare and contrast characteristics of hematite and brick 2
p. 153 Demonstrate an understanding of the radius and diameter of a circle Measure length to specified accuracy using metric units Classify metamorphic rocks by the arrangement of the grains that make up the rocks 6 p. 168-169 Use ratio and proportions to solve real-life problems Use fractions, decimals, and percents in estimations, computations, and applications Demonstrate understanding that gold and jewelry marked 12 Karat is 50% gold 6 p. 177-179 Construct and read drawings made to scale Understand that maps and globes are drawn to scale and use symbols to represent topology and other features of the Earth s surface 3
Measure to specified degree of accuracy Construct and read drawings made to scale Apply properties of rational numbers (decimal numbers) in verifying reasonableness of solutions Use decimals in estimations, computations, and applications 6 p. 188 Apply properties of ratio and proportion to solve real-life problems Compute using rational numbers (whole numbers and decimal numbers) Round decimals numbers Construct and read drawings made to scale Read and interpret USGS topographic maps Construct and read drawings made to scale 4
6 p. 195 Construct and read drawings made to scale Apply properties of ratio and proportion to solve real-life problems Apply properties of rational numbers (decimal numbers) in verifying reasonableness of solutions Demonstrate an understanding of diameter of a circle as it relates to a sphere Use a map scale to calculate actual distance 5
7 p. 204-206 Measure to specified degree of accuracy Use fractions, decimals, and percents in estimations, computations, and applications Calculate the percentage of change of a quantity Demonstrate an understanding of percent as a part of a hundred and find the percent of a number Apply formulas to real-life problem-solving Compute using rational numbers (whole numbers and decimal numbers) Collect, organize, represent real-life sets in table form Compare the rates of weathering that take place under different conditions 6
8 p. 228-229 Measure to specified degree of accuracy Collect, organize, represent real-life sets in table form Apply properties of rational numbers (decimal numbers) in verifying reasonableness of solutions Represent verbal descriptions graphically Estimate quantities graphically Construct graphs appropriate for given real-life Organize and describe distributions of in graph form Estimate measures in real-life problem solving Formulate conjectures based on direct measurement Develop and test a hypothesis about how mass movement affects the size and shape of a sand hill 7
8 p. 232 Measure length to specified accuracy using metric units Perform an experiment to determine how the force of falling raindrops affects soil 8 p. 253 Compute using rational numbers (whole numbers and decimal numbers) and verify reasonableness of solutions Use decimals, in estimations, computations, and applications Explore the effect of a severe coastal storm on the erosion of a sandy coast 8
8 p. 261 Compute using rational numbers (whole numbers and decimal numbers) and verify reasonableness of solutions Represent verbal descriptions graphically Estimate quantities graphically Construct graphs appropriate for given real-life situation Organize and describe distributions of in graph form Know, derive, and solve problems involving volume Determine how a river s volume of flow and sediment load change over a six month period 9 p. 269 Compute using rational numbers (whole numbers and decimal numbers) Discuss water-saving devices appropriate for the home 9
9 p. 272, 274 Measure in liters and milliliters to specified degree of accuracy Use fractions, decimals, and percents in estimations, computations, and applications Demonstrate an understanding of percent as a part of a hundred Read and interpret distributions expressed as graphs Compute using rational numbers (whole numbers and decimal numbers) and verify reasonableness of solutions Model the distribution of the Earth s water p. 272, 274 Analyze and compare using a variety of circle graphs Measure to specified degree of accuracy Demonstrate an understanding of percent as a part of a hundred and find the percent of a number 10
9 p. 288 Collect, organize, represent real-life sets in table form Measure mass to specified degree of accuracy Round decimals numbers Formulate conjectures based on direct measurement Apply properties of rational numbers to solve real-life problems Discover how trees help to keep water moving through the cycle 9 p. 291 Read and interpret distributions expressed as graphs Compute using rational numbers (whole numbers and decimal numbers) and verify reasonableness of solutions Justify mathematical conclusions Use percent in estimations, computations, and applications Interpret and analyze information from graphs to determine daily water usage in the U.S. 11
10 p. 298-299 Measure time to specified degree of accuracy Collect, organize, represent real-life sets in table form Find the mean (average) of a given set of Discover that increasing a stream s volume and its slope can increase the water s speed 10 p. 322-323 Measure to specified degree of accuracy Collect, organize, represent real-life sets in table form Find the mean (average) of a given set of Experiment and compare different soil types to learn more about their water-holding properties 11 p. 336 Use fractions, decimals, and percents in estimations, computations, and applications Express real-life in fractional form Apply properties of rational numbers (fractions and decimal numbers) in verifying reasonableness of solutions Understand that concentrations are measured in parts per million Express concentrations in fractional form 12
11 p. 363 Conduct an experiment to test water quality 12 p. 368 Estimate measures in real-life problem solving Demonstrate how waves formed at the surface affect deeper water 12 p. 374-376 Determine elapsed time Discover and extend mathematical/geometric patterns Construct, read, and interpret distributions expressed as graphs Apply properties of rational numbers (decimal numbers) in verifying reasonableness of solutions Explore patterns in high tides and low tides 13
12 p. 381 Estimate measures in real-life problem solving Use dimensional analysis (measures expressed as rates) to solve real-life problems Formulate conjectures based on direct measurement Compute using rational numbers and verify reasonableness of solutions Calculate the density of a substance 12 p. 382 Find the mean (average) of a given set of Estimate measures in real-life problem solving Convert measures, times, and/or temperatures Formulate conjectures based on direct measurement Explore the concept that conditions change as you descend from the surface to the ocean floor 14
12 p. 384-385 Convert measures, times, and/or temperatures Formulate conjectures based on direct measurement Graph points on a coordinate graph Measure in milliliters and liters to specified accuracy using metric units Read and interpret distributions expressed as graphs Compute using rational numbers and verify reasonableness of solutions Organize and describe distributions of using line graphs Practice the skill of controlling variables in an experiment while exploring the concept of density 15
12 p. 395 Read and interpret distributions expressed as graphs Compute using rational numbers and verify reasonableness of solutions Organize and describe distributions of using line graphs Convert measures, times, and/or temperatures Formulate conjectures based on direct measurement Construct line graphs to describe the relationship between ocean temperature and depth 13 p. 403 Construct graphs based on distributions Graph points on a coordinate graph Construct bar graphs based on distributions Explore features of the ocean floor 16
13 p. 406 Construct line graphs based on distributions Measure length to specified accuracy using metric units Model and graph characteristics of the ocean floor 13 p. 407 Construct line graphs based on distributions Read and interpret graphs Gather and graph sonar on the depth of the ocean floor; display Construct line graphs based on distributions 13 p. 423 Measure using customary units to specified degree of accuracy Explore the many natural resources of the sea (e.g., seaweed) 17
13 p. 431 Use and interpret diagrams and appropriate mathematical notation to solve problems Estimate measures in real-life problem solving Explore characteristics of the ocean floor and apply to real-life experiences p. 435 Read and interpret time schedules Determine elapsed time Compute using rational numbers and verify reasonableness of solutions Use fractions, decimals, and percents in estimations, computations, and applications Round decimals numbers Explore the transportation issues associated with waterways in the U.S. 18
14 p. 441 Read and interpret graphs based on distributions Demonstrate an understanding of percent as a part of a hundred Use decimals, and percents in estimations, computations, and applications Demonstrate an understanding that the Earth s atmosphere is made up of nitrogen, oxygen, carbon dioxide, water vapor, and other gases and particles 14 p. 444-445 Collect, organize, represent sets in table form Explore how weather factors affect the number of particles in the air 14 p. 451-455 Apply formulas to real-life problem-solving Estimate measures in real-life problem solving Measure length to specified accuracy using metric units Collect, organize, represent sets in table form Explore factors affecting air pressure and methods for measuring it 19
14 p. 458 Compute using rational numbers and verify reasonableness of solutions Estimate measures in real-life problem solving Construct line graphs based on distributions Calculate the temperature above the Earth s surface 14 p. 459 Use and interpret diagrams and appropriate mathematical notation to solve problems Explore the layers of the atmosphere 14 p. 465 Apply properties of integers to solve real-life problems Collect, organize, represent sets in table form Construct line graphs Estimate temperature in real-life problem solving Apply properties of rational numbers (decimal numbers) in verifying reasonableness of solutions Design and construct a line graph related to temperature 20
15 p. 472-473 Collect, organize, represent sets in table form Estimate temperature and time in real-life problem solving Measure in milliliters and liters to specified accuracy using metric units Convert between units of measure in the same system using conversion factors Construct double line graphs based on distributions Develop and test a hypothesis about how quickly different materials absorb radiation at different temperatures 15 p. 475-477 Estimate temperature and length in real-life problem solving Measure length to specified accuracy using metric units Construct line graphs Estimate quantities graphically Represent verbal descriptions graphically Describe how temperature is measured and name the ways heat is transferred 21
15 p. 488-489 Using a psychrometer to take dry-bulb and wet-bulb readings Use percent in estimations, computations, and applications 15 p. 495 Demonstrate an understanding of the radius and diameter of a circle Apply properties of ratio and proportion to solve real-life problems Represent powers as repeated multiplication Compute using rational numbers and verify reasonableness of solutions Measure rainfall with a rain gauge 22
15 p. 499 Apply properties of ratio and proportion to solve real-life problems Compute using rational numbers (whole numbers and decimal numbers) Construct bar graphs Estimate measures in real-life problem solving Construct a graph to display average monthly rainfall 16 p. 510 Use dimensional analysis (measures expressed as rates) to solve real-life problems Compute using rational numbers and verify reasonableness of solutions Select appropriate unit of measure for given situation Learn how to calculate the distance from a thunderstorm 23
16 p. 518-519 Collect, organize, represent real-life sets in table form Plot points (on a coordinate grid or map Track a hurricane by plotting real-life points (latitude and longitude) 16 p. 528-529 Use percent in estimations, computations, and applications Understand that a weather map is a snapshot of conditions at a particular time over a larger area 24
17 p. 544 Demonstrate an understanding of the basic elements of geometry (right angles, degrees, circles) and use appropriate geometric terminology; Apply properties of rational numbers to solve multi-step problems Estimate measures in real-life problem solving Apply properties of decimals and fractions to solve real-life problems Demonstrate an understanding of the relationship between the seasons and the tilt of the Earth 17 p. 546-547 Measure temperature to specified degree of accuracy Measure angles to specified accuracy using a protractor Demonstrate an understanding of the basic elements of geometry and use appropriate geometric terminology Construct a triple line graph Collect, organize, represent real-life sets in table form Investigate how the angle of the sun s rays affects the amount of energy absorbed by different parts of Earth s surface 25
17 p. 558-559 Read and interpret double line graphs and bar graphs based on distributions Graph and interpret related to climate; make conclusions based on tables 18 p. 585 Apply formulas to real-life problem-solving Substitute known values into literal equations or formulas and solve for unknown value Define population density as an equation and understand that population density equals the number of individuals divided by the unit area 26
18 P. 586 Find the area of a rectangle Apply formulas to real-life problem-solving Estimate measures in real-life problem solving Compute using rational numbers and verify reasonableness of solutions Estimate population size 18 p. 588 Read and interpret line graphs based on distributions Graph changes in population 27
18 p. 591 Collect, organize, represent real-life sets in table form Apply formulas to real-life problem-solving Construct line graphs Read and interpret graphs Model the mark-and-recapture method to monitor populations 18 p. 598 Read and interpret a double-line graph Analyze the results of a lab which simulates the mark-and-recapture method to monitor populations 18 p. 603 Construct a double-line graph Design and construct a line graph to display the monitoring of a deer population 28
19 p. 624 Construct bar graphs Measure length to specified accuracy using metric units Analyze which of four ecosystems receives the most precipitation yearly 19 p. 631 Read and interpret a double-line graph Interpret graphs related to climate conditions in various biomes 20 p. 647, 658 Read and interpret line and circle graphs Analyze related to world population and growth rates 20 p. 656 Demonstrate an understanding of percent as a part of a hundred Use decimals, and percents in estimations, computations, and applications Calculate the percent of the fish catch throughout the world 29
20 p. 663 Read and interpret line graphs Find area as it relates to real-life Select appropriate unit of measure for given situation Interpret graphs which display the rate of extinction of bird species 20 p. 672 Construct bar graphs Use percent in estimations, computations, and applications Represent verbal descriptions graphically Make a bar graph which compares mammals and birds that are endangered and threatened 21 p. 678 Construct circle graphs Use percent in estimations, computations, and applications Measure angles using a protractor Apply properties of ratio and proportion to solve real-life problems Make a circle graph to show the uses of energy in the U.S. 30
21 p. 680 Read and interpret bar graphs Interpret graphs which display related to oil reserves worldwide 21 p. 695 Apply properties of ratio and proportion to solve real-life problems Compute using rational numbers and verify reasonableness of solutions Estimate measures in real-life problem solving Interpret related to nuclear energy 21 p. 699 Read and interpret distributions expressed as graphs Use percent in estimations, computations, and applications Interpret that reflects break-down of U.S. electricity generated by nonrenewable fossil fuels 31
21 p. 704-705 Compute using rational numbers (whole numbers and decimal numbers) and verify reasonableness of solutions Demonstrate an understanding of percent as a part of a hundred and find the percent of a number Interpret related to the world s energy production between 1973 and 1995 21 p. 714-715 Measure to specified degree of accuracy Convert between units of measure in the same system using conversion factors Convert weights/capacities, geometric measures, times, and temperatures Apply properties of proportion to solve real-life problems Understand that scientists can express their observations through measurement in a precise and accurate manner 32
p. 722-724 Organize and describe distributions of using bar, line, and circle graphs Use proportions to solve real-life problems Graph scientific 33