These Resources (not from Math Kangaroo) may be helpful in preparing for Math Kangaroo levels 1-4.

Workbooks on Amazon:

Balance Benders  (Algebraic reasoning, all levels of MK)

Balance Math and More

Mind Benders (Logic Puzzles)

Area Mazes by Nokai Inaba

Books from the Art of Problem Solving:

Beast Academy 2B (Practice and Guide) (MK Level 1/2)

Beast Academy 4B (Practice and Guide) (MK Level 3/4)

Beast Academy Puzzle Books for grades 2, 3, and 4

Beast Academy books are excellent math enrichment overall - the ones chosen above have explicit sections on Problem Solving/Logic and visual puzzles similar to those you might find on Math Kangaroo.  

Problem Solving Books  (Solve it! Series) from the AIMS foundation.

Most of these are out-of-print and hard to find.  But I used them for the foundation of the K-3 evening problem solving Club at Azevada.  

They are designed for classroom teachers, not to be used at home, but you can often adapt the activities.   The prep work can be high, though, so this might not be the best option.  They really work best in a Math Club setting.  

On Amazon, search for "Solve It" and AIMS, and that should bring up available copies.   Here's an example:  

4th grade Solve It Book

Some are availble.

From the Public Library

 (for MK Level 1/2)

Greg Tang Math Picture Books: Grapes of Math, Math for All Seasons, Math Appeal, and many more

(for MK Levels 3+)

Socrates and the Three Little Pigs (Probability)

Card Games & Board Games:

Swish (2D visualization)

Set  (logic)

Games like Q-bitz (logic, visual reasoning)

Cat Crimes (logic puzzles)

Cloaked Cats (a game of logical reasoning)

(for levels 1/2) Games that promote flexible equation making... Sleeping Queens, Equate

Websites

3D visualizing 

Greg Tang Mental Math fluency games (Level 1/2, some for 3/4)

Math Riddles (many 3-point MK problems are like these)