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Features

  • Real sunrise and sunset times for December 21 in six cities
  • Daylight in two steps: sunrise to noon, then noon to sunset, with minutes regrouped into hours
  • Round each day to the nearest half hour and make a bar graph
  • A year of daylight in Seattle as a line graph to draw
  • The tilted Earth in December, and five cities north and south on both solstices
  • Noon shadows of a yardstick in December and June, in inches and in feet and inches
  • Six daylight word problems, the length of the night among them
  • Every page in color and in black and white
  • Answer keys included

Skills Covered

  • Find elapsed time across noon in hours and minutes
  • Regroup 60 minutes as 1 hour
  • Round a time to the nearest half hour
  • Make and read bar graphs and line graphs
  • Compare data from two halves of the world
  • Convert inches to feet and inches

About the winter solstice

Earth spins on an axis that leans about 23.4 degrees. In December the northern half of Earth leans away from the sun, so the sun stays low in the sky, days are short and shadows are long. The December solstice, on December 21, 2026 at 3:50 p.m. Eastern time, is the moment the North Pole leans farthest from the sun: the shortest day of the year in the north and the longest in the south, where it is summer. After it, northern days slowly grow longer again until the June solstice. The sunrise and sunset times in this pack are real, worked out with NOAA's solar calculator equations and checked against the US Naval Observatory.

How to Use This Pack

Six pages. Page 1 gives the sunrise and sunset in six cities on December 21: find the time from sunrise to noon, from noon to sunset, and add them, turning 60 minutes into an hour where needed. Page 2 rounds the daylight in six more cities to the nearest half hour and makes a bar graph of it. Page 3 is a year of daylight in Seattle, on the 21st of each month: plot it as a line graph and find the longest and shortest months and the two months with 12 hours. Page 4 shows the tilted Earth in December and compares five cities, north and south, on the December and June solstices. Page 5 shows a yardstick's noon shadow in New York in December and in June, drawn to scale, then compares six cities' shadows: write each December shadow in feet and inches and find how much longer it is than in June. Page 6 is six word problems. The first row or problem on pages 1, 2, 3 and 5 is worked as an example.

In the Classroom

Before page 1, look up today's sunrise and sunset for your town and work out the daylight together on a time line, as in the example. Before page 4, shine a flashlight on a tilted globe or ball in a dark room and turn it to see why the north gets less light in December. For page 5, stand a yardstick up outside at noon on a sunny day and measure its shadow, then try again near the end of the school year.

At Home

Write down the sunrise and sunset times from a weather app for a week around December 21 and find the daylight each day. Is it getting longer or shorter? On a sunny day, measure a shadow at noon now and again in spring.

Tips for Success

  • Count from sunrise up to noon first, then from noon to sunset
  • Add the hours, then the minutes; 60 minutes make 1 hour
  • A day has 24 hours, so the night is 24 hours take away the daylight
  • To round to the nearest half hour, look at the minutes
  • The lower the sun, the longer the shadow

Common Core Standards Alignment

This pack supports the following Common Core State Standards for Mathematics:

  • 2.MD.D.10 Make picture and bar graphs (one unit per square or picture) for up to four categories, and answer joining, separating and comparing questions from them.
  • 3.MD.A.1 Read and record time to the exact minute, find how many minutes pass between times, and solve story problems adding or subtracting minutes.
  • 4.MD.A.1 Know how units within one system compare, rewrite a measurement in a smaller unit, and make two-column conversion tables, like yards to feet.
  • 4.MD.A.2 Solve story problems on distance, time, liquid volume, mass and money with any operation, simple fractions or decimals and unit changes, using number-line diagrams.
  • 5.MD.A.1 Change measurements between bigger and smaller units of one system, such as 250 cm to 2.5 m, and use this in multi-step real-life problems.

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Winter Solstice Daylight Math

3rd – 5th Grade

The shortest day of the year, with real sunrise and sunset times from cities in North America, Britain and the far south. Students work out hours of daylight across noon, round and graph them, follow a year of daylight on a line graph, compare the north and the south and read noon shadows in inches and feet.

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What’s Included

  • 6 worksheets, each with a matching answer key
  • Every worksheet in color and in black and white
  • Real sunrise and sunset times, a bar graph and a line graph
  • North and south, noon shadows and 6 word problems
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This worksheet is free to download, print, copy, and hand out in your classroom or at home. You do not need to create an account, and there are no watermarks on the PDF.