Grade 5: Integers

Warm up with a quick recall on the board. Use a horizontal or vertical number line through zero (temperature, sea level) to order negatives and model moving up and down.

Integers are the whole numbers extended below zero: ..., -3, -2, -1, 0, 1, 2, 3, ... Negative numbers describe amounts less than nothing, such as a temperature below zero, a debt, or floors below ground level. The number line is the single best model, because it makes 'less than zero' and the direction of each move visible. Model the method clearly, thinking aloud:

• Anchor to real contexts first: temperatures below zero, money owed, floors in a basement, points lost in a game.
• Use a horizontal number line with zero in the middle. Moving right is adding, moving left is subtracting, whichever side of zero you start on.
• Show that -5 is less than -2, because it sits further left. This reverses the intuition that a bigger digit means a bigger number.
• Teach adding and subtracting as moves on the line: -3 + 5 lands on 2; -3 - 4 lands on -7.
• Introduce multiplying signs last, with the rule that two negatives make a positive (-3 x -2 = 6) and a positive times a negative is negative.

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the worksheet independently. Hand out the three difficulty levels below so every child works at the right stretch.

Circulate and look for these, they are the usual sticking points:

• Thinking -5 is greater than -2 because 5 is greater than 2.
• Losing track of the sign when subtracting a negative (5 - (-3) = 8, not 2).
• Assuming subtracting always makes a number smaller, which fails once negatives are involved.
• Confusing the minus sign for subtraction with the sign that marks a negative number.
• Thinking -8 is greater than -3 because 8 > 3, and losing track of direction when crossing zero.

Pull the class back together. Ask one child to explain integers in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.