Math Investigations

Help with Opening PDF Files

Chapter 3

Part 1: For the problem in the Teacher's Edition, page 58

Provide students with the Problem Worksheet (PDF file)

Have students share the different ways they wrote the addition sentences. You might even want to work with the class to list the addition sentences in an organized way to see how many different addition sentences there would be. For example,

51 + 1 = 52
50 + 2 = 52
49 + 3 = 52
48 + 4 = 52
etc.

Possible Answer:

50 + 2 = 52
2 + 50 = 52
25 + 27 = 52
20 + 32 = 52
40 + 12 = 52

There are 51 different ways to write these addition sentences.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 7 on subtracting numbers.

Introducing the Investigation

Introduce the investigation by reading aloud the assignment at the top of the fist page of the Description of Investigation and Student Report (PDF file), by having one of your students read aloud the assignment, or by having the students read the assignment individually.

Put students in groups of two to four to work on the investigation.

Doing the Investigation

Don't expect students to make a drawing to scale. Just make sure they have all of the measurements in their drawings. The numbers across the wall should total 168 inches, the width of the wall.

Possible Answer:

3 paintings 42 inches above floor, 30 inches, 42 inches, and 48 inches wide and 12 inches apart from each other and from the left and right walls

Student Report

Communicating measurements in a sketch is a very important skill in mathematics.

Extending the Investigation

Have students plan a display in your classroom of some of the paintings of students in the class. Have them draw a sketch with measurements to show how they will display the paintings.


Houghton Mifflin Math Grade 4