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Data, Prediction and Linear Functions

Exploring the History of the Universe

Objectives: Students will learn about the Big Bang theory of the universe through reading a NASA press release and viewing a NASA eClips video segment. They will use simple linear equations to analyze data that reveals the expansion and early history of the universe after the Big Bang.

Mathematics Skill or Topic Area:

Data, Prediction and Linear Functions

Next Gen Science Framework ESS1.A The universe and its stars; PS4.A Wave properties; PS4.B electromagnetic spectrum; PS4.C Information technologies and instrumentation; ETS1.A: Defining and Delimiting an Engineering Problem; ETS1.B: Developing Possible Solutions; ETS1.C: Optimizing the Design Solution

Common Core ELA for Science: RST.6-8.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.RST.6-8.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.6-8.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

Common Core Math Standard: CCS.8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities; CCS.8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables; CCS.8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Video Engagement: Hubble Wide Field Camera 3 The new Wide Field Camera allows researchers to see further in space than ever before and record objects the human eye cannot see. (6 minutes) View Program

Engage your students with a press release:

NASA'S Hubble Provides First Census of Galaxies Near Cosmic Dawn

WASHINGTON -- Using NASA's Hubble Space Telescope, astronomers have uncovered a previously unseen population of seven primitive galaxies that formed more than 13 billion years ago, when the universe was less than 4 percent of its present age. The deepest images to date from Hubble yield the first statistically robust sample of galaxies that tells how abundant they were close to the era when galaxies first formed.

The results are from an ambitious Hubble survey of an intensively studied patch of sky known as the Ultra Deep Field (UDF). In the 2012 campaign, called UDF12, a team of astronomers led by Richard Ellis of the California Institute of Technology in Pasadena used Hubble's Wide Field Camera 3 (WFC 3) to peer deeper into space in near-infrared light than any previous Hubble observation.

The observations were made during six weeks in August and September, and the first scientific results now are appearing in a series of scientific papers.

The results show a smooth decline in the number of galaxies looking back in time to about 450 million years after the big bang. The observations support the idea galaxies assembled continuously over time and also may have provided enough radiation to reheat, or re-ionize, the universe a few hundred million years after the theorized big bang.

Looking deeper into the universe also means peering further back in time. The universe is estimated to be 13.7 billion years old. The newly discovered galaxies are seen as they looked 350 to 600 million years after the big bang. Their light is just arriving at Earth now.

Astronomers study the distant universe in near-infrared light because the expansion of space stretches ultraviolet and visible light from galaxies into infrared wavelengths, a phenomenon called "redshift." The more distant a galaxy, the higher its redshift.

The greater depth of the new Hubble images, together with a carefully designed survey strategy, allows this work to go further than previous studies, thereby providing what researchers say is the first reliable census of this epoch. Notably, one of the galaxies may be a distance record breaker, observed 380 million years after the birth of our universe in the big bang, corresponding to a redshift of z = 11.9.

A major goal of the new program was to determine how rapidly the number of galaxies increases over time in the early universe. This measure is the key evidence for how quickly galaxies build up their constituent stars.

Press release date line - December 12, 2012

Press release location: [ Click Here ]

Explore math connections with


Problem I - Our Expanding Universe! - Students plot data for the speeds and distances of galaxies and learn about Hubble's Law for the expanding universe. Then they use a linear equation to make estimates from this data. [ Open PDF ]

Problem II - Exploring Infant Galaxies - Students learn about the cosmological redshift, z, and use this variable to calculate the temperature of the universe, the expansion of space, and the look-back time for distant objects. [ Open PDF ]

Explain your thinking:

Write your own problem - Using information found in the Math Connection problems, the press release or the video program, create your own math problem. Explain why you set the problem up this way, and how you might find its answer.

Evaluate your understanding:

Challenge Problem -

    Supermassive Black Holes
Students explore two linear equations for the growth of black holes during different eras in the history of the universe. They then create a mathematical model and infer how a recently discovered supermassive black hole has grown so large. [ Open PDF ]



3-D Solar System

Extend your new knowledge - Students visit the Voyager 1 and Pioneer 10 spacecraft, estimate their light-travel distances from each other, compare this to the distance to the nearest star, and explore expanding space. [ Open PDF ]